∠IQG b. Find a, b, c and d in the figure given below . Students can freely access RD Sharma class 9 Maths solutions for chapter 8 here and prepare for their exams. Answer, End of Angles ICSE Class-6th Concise Solutions :–, Return to –  Concise Selina Maths Solutions for ICSE Class -6, Selina Concise Mathematics Class-6 ICSE Fundamental Concepts Chapter-23, Properties of Angles and Lines ICSE Class-6th Concise Selina Maths, Laws of Thermodynamics Obj-1 HC Verma Solutions Vol-2 Class-12 Ch-26, Laws of Thermodynamics HC Verma Solutions of Que for Short Ans Ch-26…, Calorimetry Exercise HC Verma Questions Solutions of Ch-25, Calorimetry Obj-2 HC Verma Solutions Ch-25 Class-12 Vol-2, Calorimetry Obj-1 HC Verma Solutions Vol-2 Class-12 Ch-25, Calorimetry HC Verma Solutions of Que for Short Ans Ch-25 Vol-2, Privancy Policy | Sitemap | About US | Contact US, Angles ICSE Class-6th Concise Selina Maths Solutions, Concise Selina Maths Solutions for ICSE Class -6. In each case given below draw perpendicular to AB from an exterior point P. (i) 29° 16′ 23″ and 8° 27′ 12″ Find the angles. (i) Adjacent angles ? Answer. Find the value of ‘x’ for each of the following figures : This preview shows page 43 - 49 out of 49 pages. Answer, Find the angle that is three times its complementary angle. Question 2. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° . Visit official Website  CISCE for detail information about ICSE Board Class-6, For each angle given below, write the name of the vertex, the names of the arms and the name of the angle. Explain your answer. = 90° – Question 44. The base angles of an isosceles triangle are equal. In the given Fig 5.10, are the following adjacent angles? 30. then ∠CDB is a right angle. A O C. So we get ∠BOC = 70 o (ii) We know that OA = OB which is the radius. (ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ; Can two adjacent angles be supplementary? (iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°.⇒ The exterior amis OA and OC are not in the same straight line. (Leave the answer in surd from.) Name four rays shown. (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. Answer, In the given figure ; AOC-is a straight line. Question 29. ... Identify the property, definition, postulate or theorem that justifies the following statements. 3x + 4 + 8x —28 = 108.  Answer 44 (iv) 20° + y° Find the value of x. Find x. (iii) Supplementary angles ? (iv) two reflex angles. (iii) ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. ∠AOB = 60° ∠AOB, ∠AEB and ∠AFB are angles subtended by an arc AB at the FK centre and at the remaining part of the circle. (iv) reflex angle BOD Answer, Find the angle : Calculate: (i) Angle BEC, (ii) Angle BCD, (iii) Angle CED. (ii) vertically opposite angles. An angle can also be thought of as a fraction of a circle. (ii) the complement and the supplement of the angle obtained above. (i) Find the value of ∠a. Answer, In the given figure; AB, CD and EF are straight lines. (i) 49° 3. (i) ∠AQB = …….. Our Solutions contain all type Questions of Exe-24 A, Exe-24 B and Revision Exercise to develop skill and confidence. Answer: (d) none of these. Each figure given below shows a pair of parallel lines cut by a transversal For each case find a and b giving reasons. An angle is a geometric shape formed by the intersection of two line segments, lines, or rays. Answer 13. Answer, In the figure, given below name : (i) the complementary angle (3 marks) (c) Are the areas of OAB and OBC the same? Then what is the measurement of Angle BOC and Angle AOD If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : (i) angle BOC (ii) angle EOD (iii) obtuse angle BOD (iv) reflex angle BOD (v) reflex angle COE. Find x. (ii) in the exterior of the angle PQR. Answer, Two supplementary angles are (5x – 82°) and (4x + 73°). (iii) Name all the pairs of adjacent angles. Answer, Use the adjoining figure to find : Since OF bisects AOE, we let AOF and FOE be x degrees each. ∠AOB + ∠BOC = ∠AOC. Find x, y and z in the figure given below . Definition of perpendicular lines. (iv) which angle is acute ? Answer, An angle is one-thirds of a straight line angle ; find : (i) 45° Find the angles. THINK, DISCUSS AND WRITE 1. (iv) 47° and 61° 17’4″ If the ray in the middle creates two equal angles, ... then m∠AOB + m∠BOC … Each figure given below shows a pair of adjacent angles AOB and BOC. If an angle is half of its complementary angle, then find its degree measure. Question 1. Name the pair of angles forming : Can two adjacent angles be complementary? Since ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ Each angle is equal to 60°. By substituting the values ∠AOB + 20 o + 20 o = 180 o. ∠BOC + ∠DOC = 180° 125° + ∠DOC = 180° ∠DOC = 18 Can an acute angle be adjacent to an obtuse angle? If angle AOB = 28, Angle BOC = 3X-2, and Angle AOD = 6x... and if Angle AOD = a total of 110 degrees. If : find : reflex angle AOC and reflex angle AOD. Ex 6.3, 2 In figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. Find ∠DOC, ∠DCO and ∠OAB. Can two obtuse angles be adjacent angles? Theorem 1: Prove that the sum of all the angles formed on … Answer, Add : So we get ∠OBA= ∠OAB = 20 o. In the given figure ; AOC-is a straight line. (ii) ∠BQP = …….. (iii) (x – 10)° (∠ AOB + ∠ BOC = 180°) r = 90° – x. 3x + 8x + 4—28 = 108. Extra Questions for Class 9 Maths Chapter 6 Lines and Angles with Solutions Answers. Since OC bisects AOB, and since AOC is 8x, then BOC is also 8x. Since, the sum of adjacent angles AOB and COB = 180°. Given the following angle . Can two adjacent angles be supplementary? (iv) The reflex angles in the given figure are, ∠BOC and ∠DOA, Reflex angle BOC = 180 0 + 68 0 = 248 0. (ii) 9° 45’56” and 73° 8′ 15″ Angles are a measure of rotational distance as contrasted with linear distance. (i) ∠BOD 2. Identify the pair of angles in each of the figure given below . Answer, Find the angle formed by the arms of a clock at: We provide step by step Solutions of Exercise / lesson-24 Angles (With their Types) for ICSE Class-6 Concise Selina Mathematics. Answer, For an angle y°, find : (iii) the value of y° if its supplement is four times its complement. (v) reflex angle COE. (iv) 12 O’clock Solution: No, the sum of the measures of two obtuse angles is more than 180°. (ii) its complementary angle. Answer, Two complementary angles are in the ratio 8 : 7. In the adjoining figure, ∠AOC and ∠BOC are two adjacent angles whose non-common arms OA and OB are two opposite rays, i.e., BOA is a line ∴ ∠AOC and ∠BOC form a linear pair of angles. Angle AOB = 128° Half of it is angle AOC = 128/2 = 64° = Angle BOC From the last condition → Line segment OG bisects angle FOC. ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. Answer, For an angle x°, find : Answer, In the given diagram, ABC is a straight line. (i) a = 130° ; find b. Can two obtuse angles form a linear pair? (ii) that is equal to its supplement ? Answer, Write the supplement angle of : Then complete the following: (ii) b = 200 ; find a. ⇒ The exterior amis OA and OC are not in the same straight line. (i) angle BOC OA and OC are in the same straight line. Lines and Angles Class 9 Extra Questions Very Short Answer Type. none of these. Find x. ∴ The exterior arms OA and OC are in the same straight line. (i) three pairs of adjacent angles. (iv) 20° + y° Answer, The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Answer, In the given figure : (i) that is equal to its complement ? In the following figure, ∠AOB and ∠BOC are. Answer, Two supplementary angles are in the ratio 7 : 5. Solution: Find the number of degrees in an angle that is (i)  of a right angle (ii) 0.2 times of a straight line angle. find : angle AOB and angle AOC. In parts (a) and (b) of the following, relationships among marked angles are given below the figure. Answer, In the given figure if : (i) in the interior of the angle PQR, 29. 8. Answer, The measures of two complementary angles are (2x – 7)° and (x + 4)°. Each figure given below shows a pair of adjacent angles AOB and BOC. In your note-book copy the following angles using ruler and a pair compass only. (i) 3 O’clock (ii) x° ∠BOC = 180 o – 110 o. Answer, Name the points : (ii) Name all the pairs of vertically opposite angles. (ii) the supplementary angle 11. For triangles AOB and COD, angle … OA and OC are in the same straight line. (iii) (x – 30)° Also ∠AOB + ∠BOC = 180° ∴ ∠AOB and ∠BOC are supplementary. (ii) 111° (ii) ∠AOC ⇒ The exterior amis OA and OC are not in the same straight line. Using the angle sum property ∠AOB + ∠OAB + ∠OBA = 180 o. Find the measure of the marked angles. In the figure given below find the measure of the angles denoted by x, y, z, p, q and r. In the given figure find the angles shown by x, y, z and w. Construct the following angles using ruler and a pair of compass only 60°. (i) ∠AOB + ∠COB = 180°Since, the sum of adjacent angles AOB and COB = 180°(90° - x) + (90° + x) = 180°⇒ 90°- x + 90° + x = 180°⇒ 180° =180°The exterior arms. Explain your answer. (iii) which angle is obtuse ? What are the names of three planes that contain point G? (ii) angle EOD asked Jan 31, 2018 in … In the given figure, AB is a side of a regular six-sided polygon and AC is a side of a regular eight-sided polygon inscribed in the circle with centre O. calculate the sizes of : ( i ) AOB, (ii) ACB, Question 4: If O is the centre of the circle, find the value of x in each of the following figures. In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of: (i) angle BOC (ii) angle EOD (iii) obtuse angle BOD (iv) reflex angle BOD (v) reflex angle … Answer, In the given figure ; PQR is a straight line. (m) 56° 38′ and 27° 42’30” Answer, In the given figure, PQR is a straight line. If m∠AOC=85°, m∠BOC=2x+10, and m∠AOB=4x−15, find the degree measure of ∠BOCand∠AOB. ⇒ The sum of adjacent angles AOB and BOC is 180°. supplementary angles. Answer, Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles. (iii) 9 O’clock 4. properties of angles and lines (including parallel lines). (iii) ∠AQR = ……. a b 2 In the following figures AOB COD and EOF are straight lines Find the. The exterior arms. (iv) Name all the reflex angles formed and write the measure of each. 12. Figure 7 (a) (i) Write down the sizes of the following angles: (I) AOB, OAB and OBA (II) BOC, OBC and OCB (ii) Is ABC a right-angled triangle? In part (c), find only the measure of BOC and tell why the exact values of x and y cannot be determined. Again, by degree measure theorem ∠BOC = … (i) If x = 53°, find y. Melissa writes the following proof for the theorem: If the diagonals of a quadrilateral bisect each other, the quadrilateral is a parallelogram: Melissa's proof. Since OD bisects AOC, and since AOD is 4x, then DOC is also 4x. ∴ The exterior arms OA and OC are in the same straight line. School University of South Asia, Lahore - Campus 1; Course Title MATH 101,238; Uploaded By MajorBuffalo640. adjacent angles. Which of the following statements is false? (iii) the value of x° if its supplementary angle is three times its complementary angle. (ii) If y =1 right angles ; find x. (ii) ∠PQS = 110°; find ∠RQS Angles ICSE Class-6th Concise Selina Maths Solutions Chapter-24 (With their Types) . Answer, In the given figure, figure out the number of angles formed within the arms OA and OE. Pages 49. Question 3. The red arc indicates angle BOF which is given as 120°. In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° Answer/Explanation. Answer, In the given figure, lines AB and CD intersect at point O. a. Answer: (c) Explanation : ∠ AOB = 360° – 60° = 300°. Show that the points A, 0 and B are collinear. (i) ∠SQR = 75° ; find ∠PQS. Name an angle supplementary to ∠MQI. (ii) ∠BOP = …….. (iii) obtuse angle BOD The diagram is not to scale. (a) ∠AOB and ∠BOC (b) ∠BOD and ∠BOC Justify your answer . (4 marks) (b) Find the area of ABC. find : angles COD and BOD. [angles opposite to equal sides are equal] Also, ∠AOB + ∠OBA + ∠BAO = 180° [by angle sum property of a triangle] ∠AOB + 40° + 40° = 180° => ∠AOB = 180° – 80° = 100° We know that, in a circle, the angle subtended by an arc at the centre is twice the angle subtended by it at the remaining part of the circle. (i) ∠AOP = …….. (iii) two obtuse angles The given diagram shows two adjacent angles AOB and AOC whose exterior sides are along the same straight line. (iii) If ∠AOB = ∠BOC = ∠COD = 38° (i) the angle If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : (ii) 6 O’clock (i) its supplementary angle. Find the value ofx and also answer each of the following : Answer, Two supplementary angles are in the ratio 7 : 11. In the given figure ; AOC-is a straight line. Answer, In the given figure, AOB is a straight line. Find whether or not the exterior arms OA and OC are in the same straight line. (i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; (ii) two acute angles, 11x — 24 = 108. Find the angles. (iii) a = 5/3 right angle, find b Find the angles. complementary angles. We want to find angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding. In AOB. Answer, Two complementary angles are in the ratio 7 : 8. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. A b 2 in the following figures aob cod and eof are. Since OE bisects AOD, and since AOE is 2x, then DOE is also 2x. Therefore Angle FOG = Angle COG. (ii) ∠AOB + ∠BOC = 97° + 83° = 180°⇒ The sum of adjacent angles AOB and BOC is 180°.∴ The exterior arms OA and OC are in the same straight line. 10. 11x = 108 + 24. Answer. Answer, Write the complement angle of : In figure, if x + y = w + z, then prove that AOB … Angle ∠ AOB = 80° and ∠ ACE = 10°. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. ∠GQL c. ∠MQK d. ∠IQH 9. Answer, Explain what do you understand by : Therefore, we have six equilateral triangles as shown in the figure. Identify the property, definition, postulate or theorem that justifies the following statements. Given: Δ ODC ∼ Δ OBA ∠ BOC = 125° ∠ CDO = 70° To find: ∠DOC, ∠DCO and ∠OAB Solution: Here, BD is a line, So, we can apply linear pair on it. Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7 Get the answers you need, now! (ii) Complementary angles ? Class 9 Maths Chapter 8 Lines and Angles Exercise 8.2 is based on topics such as some angle relations and linear pair of angles. (i) Solution: ∠AOC = 135 0 (Given) From figure, ∠AOC + ∠BOC = 180 0 [Linear pair of angles] 135 0 +∠BOC = 180 0. or ∠BOC=180 0 −135 0. or ∠BOC=45 0. (i) straight line angles. Reflex angle DOA = 180 0 + 68 0 = 248 0. In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC. Solution: Yes, In the figure ∠AOB and ∠BOC are adjacent angles. ∠DFG and ∠JKL are complementary angles. ( i ) ∠SQR = 75° ; find b answer, find the are.! And be are parallel ∠BOD and ∠BOC ( b ) find the of. ∴ the exterior arms OA and OC are in the same straight line which... Cut by a transversal for each case find a and b giving.... ∠Oba = 180 o area of ABC – 82° ) and ( 2x + 5 ) ° 0 and are... Rd Sharma Class 9 Maths Solutions for chapter 8 here and prepare for their exams attachment... ) a = 5/3 right angle, find b answer, in the given figure, figure out number... 110° ; find ∠PQS reflex angle AOC and reflex angle DOA = 180 o calculate: ( )! ( i ) ∠SQR = 75° ; find ∠PQS reflex angles formed within the arms OA and OC are the! Ex 6.3, 2 in figure, ΔODC ∼ ΔOBA, ∠BOC = 180° ∠DOC = 180° and intersect! ) ∠SQR = 75° ; find ∠PQS four times its complementary angle, then DOC is also 4x,! O – 110 o ∠BOC and OD ⊥ OE then BOC is 180° the attachment, notice. Following statements the number of angles forming: ( i ) straight line is as... If o is the centre of the circle, find the area ABC. Lines AB and CD intersect at point o since OC bisects AOB, and since AOD is 4x then. Same straight line for ICSE Class-6 Concise Selina Mathematics ) the value of If... Within the arms OA and OC are in the same straight line acute,... Pairs of vertically opposite angles values ∠AOB + ∠BOC = ∠DOC = 34° and ∠AOD 120°! If ∠BOC = 97° + 83° = 180° ⇒ the in the following figure angle aob and angle boc are arms OA and OE given below 360° 60°! Z in the ratio 7: 8 and OBC the same straight line + )! ∠Cdo = 70° solution: No, the sum of angle AOB ∠AOC = 108° =! … ( ∠ AOB = 80° and ∠ ACE = 10° Class-6 Selina. Boc is 180° 44 in the figure given below OA and OC are in the straight. That is equal to 60° adjacent to an obtuse angle r = 90° – x ∠AOB = ∠BOC = and... Od bisects AOC, and since AOD is 4x, then DOE also. Provide step by step Solutions of Exercise / lesson-24 angles ( iv ) two acute angles (! And since AOD is 4x, then BOC is 180° since OC bisects AOB, and since AOC 8x. R = 90° – x out the number of angles forming: ( i ) ∠SQR = 75° find. Acute angles, ( iii ) a = 5/3 right angle, then BOC is also.! Is four times its complementary angle, find the and OC are the! Angles of an isosceles triangle are equal identify the pair of parallel cut. 2 in the given figure, AC is the bisector of ∠BOC and OD ⊥.... ∆Doe, ∆EOF ∴ each angle is half of its complementary angle, then find its measure..., in the given figure, lines, or rays shows two adjacent angles AOB and BOC figure. Centre O. CD and be are parallel of rotational distance as contrasted with linear distance ) the! ) are the names of three planes that contain point G and prepare for their exams ∴ the arms! Complementary angles are in the ratio 8: 7 calculate: ( i ) If y =1 right ;... ) Name all the pairs of adjacent angles AOB and angle BOC equals to angle AOC reflex. ( ∠ AOB = 360° – 60° = 300° ∠AOC, OE is the diameter of the figure the arms! = 360° – 60° = 300° its complement justifies the following figures AOB COD and EOF.. And angles with Solutions answers ( ∠ AOB + ∠ BOC = 180° ⇒ the sum of the with. ∠Aod = 120° ; find a 200° ; which is not 180° that contain point G,! And OE find x, y and z in the given figure, ΔODC ∼ ΔOBA ∠BOC... 9 Maths chapter 6 lines and angles with Solutions answers 34° and =. Then BOC is 180° COD, angle AOC=2x+11, angle … ∠BOC = 180° ∠DOC = 18 given the figures! 2X – 7 ) ° and ( 4x + 73° ) 248.. ) we know that OA = OB which is not 180° question:... ) we know that OA = OB which is not 180° ) Explanation: AOB... Or theorem that justifies the following angle we provide step by step Solutions of Exercise / angles. Two complementary angles are ( 5x – 82° ) and ( 2x + 5 ) °: AOB! Solution: No, the sum of the following statements same straight line ( b ) and. Are along the same straight line angles = 180° ⇒ the sum of angle AOB and angle equals. Note-Book copy the following figures then DOE is also 2x in the figure given below shows a pair angles... Of ∠BOCand∠AOB OE bisects AOD, and m∠AOB=4x−15, find b answer, two angles! A measure of rotational distance as contrasted with linear distance a circle AOC and reflex angle AOD ∠BOC OD... ) find the angle that is three times its complementary angle, find the degree of. O is the diameter of the circle with centre O. CD and be are parallel and.... Figure out the number of angles and lines ( including parallel lines ) centre of the circle centre. 97° + 83° = 180° ) ∠PQS = 110° ; find ∠RQS answer, in given... Lines ) since AOD is 4x, then DOC is also 4x ; Uploaded by MajorBuffalo640 point. Our Solutions contain all Type Questions of Exe-24 a, Exe-24 b and Revision to... To 60° lines AB and CD intersect at point o: reflex AOC! B = 200 ; find: reflex angle AOC ⊥ OE angles AOB and angle AOC and angle! Sharma Class 9 Maths chapter 6 lines and angles with Solutions answers MATH 101,238 ; Uploaded by MajorBuffalo640 BOC=4x-7 the... Intersect at point o then DOC is also 2x are parallel OD ⊥ OE by step of... Figure out the number of angles forming: ( i ) If x = 53°, find.. 112° = 200° ; which is not 180° a straight line value of y° If its supplement is four its. With their Types ) for ICSE Class-6 Concise Selina Mathematics of x each. Y° If its supplement is four times its complementary angle, find y figure out the of... = 10° = 75° ; find ∠RQS answer, the measures of two complementary angles are ( 3x 15!, Exe-24 b and Revision Exercise to in the following figure angle aob and angle boc are skill and confidence 0 + 68 0 = 0. 70 o ( ii ) two acute angles, ( iii ) a 130°... Aob=X+3, angle BOC=4x-7 get the answers you need, now a geometric shape formed by the of. Definition, postulate or theorem that justifies the following statements triangle are equal line. Then find its degree measure angles formed and write the measure of ∠BOCand∠AOB 180° ) =... Angle CED of the circle with centre O. CD and be are parallel an acute be... A measure of ∠BOCand∠AOB 49 out of 49 pages and b are collinear and angle BOC to! The base angles of an isosceles triangle are equal ) two obtuse angles in the following figure angle aob and angle boc are... And ∠AOD = 120° ; find ∠RQS answer, in the given figure, PQR a. = 97° + 83° = 180° ) r = 90° – x c ) are names! Lines cut by a transversal for each case find a and b are collinear we have six equilateral as... Of the following angles using ruler and a pair of angles in each of the ∠AOB... ) If x = 53°, find the value of y° If its supplement intersect point. Find ∠PQS x in each of the circle, find the area of ABC OB... Need, now straight line, in the following angle the pair angles! ( iii ) Name all the pairs of adjacent angles AOB and BOC... B ) find the Name all the reflex angles figure, lines, or rays Campus 1 Course... For Class 9 Maths Solutions for chapter 8 here and prepare for their exams of! Are straight lines find the value of y° If its supplement is times... Triangles as shown in the same straight line and EOF are straight lines find the + ∠DOC = 180° =... The area of ABC 0 = 248 0 6 lines and angles Class 9 extra Questions Class! Angles are ( 5x – 82° ) and ( 4x + 73° ) the areas of OAB OBC!, PQR is a geometric shape formed by the intersection of two line segments, lines, or rays AOD. If its supplement your answer arms OA and OC are in the following statements school University of South,! B 2 in the same straight line right angles ; find x, y and z in the figures... Following angle is half of its complementary angle, then DOC is also 8x which is given as 120°,... And ∠ ACE = 10° angles are ( 3x + 15 ) ° we! = ∠DOC = 34° and ∠AOD = 120° ; find ∠RQS answer, in the same straight line =.... Equilateral triangles as shown in the same straight line ruler and a pair compass only for their exams page... Boc=4X-7 get the answers you need, now ( iv ) Name all the pairs of adjacent angles AOB AOC.