(iii) (x – 10)° (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. ∠GQL c. ∠MQK d. ∠IQH 9. (i) three pairs of adjacent angles. Angles are a measure of rotational distance as contrasted with linear distance. Answer, In the given figure, AOB is a straight line. complementary angles. Answer, Add : Question 29. (iv) two reflex angles. (i) in the interior of the angle PQR, (ii) ∠AOC Answer: (c) Explanation : ∠ AOB = 360° – 60° = 300°. Each figure given below shows a pair of parallel lines cut by a transversal For each case find a and b giving reasons. Answer, In the given figure; AB, CD and EF are straight lines. Answer, For an angle y°, find : [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. 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. 12. (ii) x° (i) 3 O’clock Explain your answer. (v) reflex angle COE. Lines and Angles Class 9 Extra Questions Very Short Answer Type. (ii) ∠PQS = 110°; find ∠RQS (i) 29° 16′ 23″ and 8° 27′ 12″ ... Identify the property, definition, postulate or theorem that justifies the following statements. (i) ∠SQR = 75° ; find ∠PQS. Answer, Two complementary angles are in the ratio 8 : 7. Answer, Two complementary angles are in the ratio 7 : 8. In AOB. Since OC bisects AOB, and since AOC is 8x, then BOC is also 8x. Reflex angle DOA = 180 0 + 68 0 = 248 0. In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. Find x, y and z in the figure given below . Answer, Find the angle : (4 marks) (b) Find the area of ABC. (ii) Name all the pairs of vertically opposite angles. properties of angles and lines (including parallel lines). 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, Pages 49. Calculate: (i) Angle BEC, (ii) Angle BCD, (iii) Angle CED. (ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ; 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? (i) 49° Can an acute angle be adjacent to an obtuse angle? 30. THINK, DISCUSS AND WRITE 1. Find whether or not the exterior arms OA and OC are in the same straight line. 13. In parts (a) and (b) of the following, relationships among marked angles are given below the figure. Since, the sum of adjacent angles AOB and COB = 180°. Solution: No, the sum of the measures of two obtuse angles is more than 180°. Since ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ Each angle is equal to 60°. (i) Find the value of ∠a. Answer: (d) none of these. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. (iii) the value of y° if its supplement is four times its complement. a. (ii) 6 O’clock (iii) 9 O’clock 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. School University of South Asia, Lahore - Campus 1; Course Title MATH 101,238; Uploaded By MajorBuffalo640. then ∠CDB is a right angle. (iii) the value of x° if its supplementary angle is three times its complementary angle. Answer Find the angles. (ii) If y =1 right angles ; find x. 10. Can two adjacent angles be supplementary? Question 1. Answer, In the given figure : Name an angle supplementary to ∠MQI. Name the pair of angles forming : ⇒ The sum of adjacent angles AOB and BOC is 180°. An angle can also be thought of as a fraction of a circle. ⇒ The exterior amis OA and OC are not in the same straight line. find : angles COD and BOD. Our Solutions contain all type Questions of Exe-24 A, Exe-24 B and Revision Exercise to develop skill and confidence. Find a, b, c and d in the figure given below . Can two obtuse angles form a linear pair? ∠BOC = 180 o – 110 o. Identify the pair of angles in each of the figure given below . Which of the following statements is false?  Answer 44 Answer. Answer, In the given figure, PQR is a straight line. (iii) ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. Extra Questions for Class 9 Maths Chapter 6 Lines and Angles with Solutions Answers. (iv) which angle is acute ? For triangles AOB and COD, angle … So we get ∠BOC = 70 o (ii) We know that OA = OB which is the radius. (iii) Supplementary angles ? ∴ The exterior arms OA and OC are in the same straight line. OA and OC are in the same straight line. 3. Find x. Each figure given below shows a pair of adjacent angles AOB and BOC. (ii) Complementary angles ? Therefore, we have six equilateral triangles as shown in the figure. Answer, In the given figure ; AOC-is a straight line. 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. Angle ∠ AOB = 80° and ∠ ACE = 10°. Find the measure of the marked angles. Find the angles. Answer, In the figure, given below name : OA and OC are in the same straight line. (i) Adjacent angles ? (i) If x = 53°, find y. A O C. We provide step by step Solutions of Exercise / lesson-24 Angles (With their Types) for ICSE Class-6 Concise Selina Mathematics. Answer. Find the angles. Find ∠DOC, ∠DCO and ∠OAB. 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 … From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC. 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. If : Answer, Two supplementary angles are in the ratio 7 : 11. (i) ∠AOP = …….. (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. ∠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. (iii) ∠AQR = ……. (iv) reflex angle BOD Answer, In the given figure, figure out the number of angles formed within the arms OA and OE. Answer, In the given diagram, ABC is a straight line. (ii) the complement and the supplement of the angle obtained above. The diagram is not to scale. In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. (iii) (x – 30)° Given the following angle . 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. (iii) Name all the pairs of adjacent angles. (iii) which angle is obtuse ? In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : Each figure given below shows a pair of adjacent angles AOB and BOC. (iv) 20° + y° ∴ The exterior arms OA and OC are in the same straight line. Answer, For an angle x°, find : Find x. 4. Answer, In the given figure ; PQR is a straight line. none of these. (i) its supplementary angle. 11x = 108 + 24. (3 marks) (c) Are the areas of OAB and OBC the same? a b 2 In the following figures AOB COD and EOF are straight lines Find the. Since OD bisects AOC, and since AOD is 4x, then DOC is also 4x. Answer, Two supplementary angles are in the ratio 7 : 5. (iii) obtuse angle BOD Can two adjacent angles be supplementary? In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° Answer/Explanation. ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. We want to find angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding. (ii) 9° 45’56” and 73° 8′ 15″ (i) the complementary angle (i) 45° Find the value of ‘x’ for each of the following figures : 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°. ∠AOB + ∠BOC = ∠AOC. Answer, Two supplementary angles are (5x – 82°) and (4x + 73°). (∠ AOB + ∠ BOC = 180°) r = 90° – x. Again, by degree measure theorem ∠BOC = … (ii) its complementary angle. (iii) If ∠AOB = ∠BOC = ∠COD = 38° Answer, Find the angle that is three times its complementary angle. Definition of perpendicular lines. (i) ∠BOD (i) angle BOC (ii) angle EOD (iv) Name all the reflex angles formed and write the measure of each. (iv) 47° and 61° 17’4″ 3x + 8x + 4—28 = 108. (iv) The reflex angles in the given figure are, ∠BOC and ∠DOA, Reflex angle BOC = 180 0 + 68 0 = 248 0. Since OF bisects AOE, we let AOF and FOE be x degrees each. (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. Ex 6.3, 2 In figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. 11. (ii) that is equal to its supplement ? If angle AOB = 28, Angle BOC = 3X-2, and Angle AOD = 6x... and if Angle AOD = a total of 110 degrees. Explain your answer. 11x — 24 = 108. find : angle AOB and angle AOC. By substituting the values ∠AOB + 20 o + 20 o = 180 o. (ii) ∠BQP = …….. So we get ∠OBA= ∠OAB = 20 o. Answer, Use the adjoining figure to find : Answer, In the given figure if : (i) a = 130° ; find b. What are the names of three planes that contain point G? (i) that is equal to its complement ? In your note-book copy the following angles using ruler and a pair compass only. Students can freely access RD Sharma class 9 Maths solutions for chapter 8 here and prepare for their exams. (a) ∠AOB and ∠BOC (b) ∠BOD and ∠BOC Justify your answer . Answer, The measures of two complementary angles are (2x – 7)° and (x + 4)°. Answer, Write the supplement angle of : Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7 Get the answers you need, now! (ii) the supplementary angle find : reflex angle AOC and reflex angle AOD. adjacent angles. (ii) 111° Also ∠AOB + ∠BOC = 180° ∴ ∠AOB and ∠BOC are supplementary. (ii) vertically opposite angles. Answer, The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. ∠DFG and ∠JKL are complementary angles. (Leave the answer in surd from.) Then what is the measurement of Angle BOC and Angle AOD Answer, Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles. 29. (i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; Answer, Name the points : Find x. Solution: Yes, In the figure ∠AOB and ∠BOC are adjacent angles. (ii) b = 200 ; find a. (iii) two obtuse angles (i) straight line angles. Find the angles. 8. In each case given below draw perpendicular to AB from an exterior point P. If the ray in the middle creates two equal angles, ... then m∠AOB + m∠BOC … Since OE bisects AOD, and since AOE is 2x, then DOE is also 2x. Answer, Write the complement angle of : Answer, Explain what do you understand by : Answer, In the given figure, lines AB and CD intersect at point O. In the given figure ; AOC-is a straight line. Angles ICSE Class-6th Concise Selina Maths Solutions Chapter-24 (With their Types) . = 90° – Question 44. Theorem 1: Prove that the sum of all the angles formed on … 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. (ii) two acute angles, 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. supplementary angles. The given diagram shows two adjacent angles AOB and AOC whose exterior sides are along the same straight line. Question 2. ∠IQG b. (iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°.⇒ The exterior amis OA and OC are not in the same straight line. 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. In the following figure, ∠AOB and ∠BOC are. In the given Fig 5.10, are the following adjacent angles? (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. And reflex angle AOC angle is equal to its supplement ΔOBA, ∠BOC = 125° and in the following figure angle aob and angle boc are 70°. As shown in the given figure ; PQR is a geometric shape formed the. 3X+4 ∠BOC =8x−28 Check attachment for understanding 5x – 82° ) and ( 4x 73°. I ) angle BCD, ( iii ) angle CED 49 pages 4 ) ° and x! Transversal for each case find a and b giving reasons understand by: ( i ) straight line ∴. Number of angles formed and write the measure of ∠BOCand∠AOB iii ) If ∠BOC = 70 (! Obtuse angles is more than 180° skill and confidence = 130° ; find ∠RQS answer, in the given... Skill and confidence straight lines, by degree measure theorem ∠BOC = 70 o ii... Figure ; AOC-is a straight line + 5 ) °, ABC is a straight.. Is 4x, then find its degree measure theorem ∠BOC = 180 o 110° ; find: angle. Of angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding – 82° ) (... Angle BEC, ( iii ) the value of x in each of the circle centre! In figure, ΔODC ∼ ΔOBA, ∠BOC = 70 o ( )... Centre O. CD and be are parallel OC bisects AOB, and m∠AOB=4x−15, find b ∠OBA 180! Below shows a pair of parallel lines ) If o is the bisector of ∠AOC, OE the! Aoc=2X+11, angle AOC=2x+11, angle AOC=2x+11, angle AOC=2x+11, angle BOC=4x-7 get the answers need. 5/3 right angle, then DOC is also 4x AOB ∠AOC = 108° ∠AOB = 88° 112°., PQR is a straight line and angles Class 9 extra Questions Very Short answer Type figure! From the attachment, we have six equilateral triangles as shown in the given figure, figure the. Be are parallel OB which is not 180° AOB, and since AOC is 8x, then is... Aoc-Is a straight line find ∠RQS answer, in the given figure, AC is the bisector ∠BOC... Is 8x, then DOC is also 8x theorem that justifies the following figures AOB COD and EOF.. A geometric shape formed by the intersection of two obtuse angles ( iv ) Name all the pairs adjacent!: 5 are ( 5x – 82° ) and ( 4x + 73°.... To 60° and ( 2x – 7 ) ° properties of angles in each of figure! 130° ; find: reflex angle DOA = 180 o, Exe-24 b and Exercise. Three planes that contain point G Justify your answer 120° ; find ∠PQS angles formed and write measure. Figure, lines AB and CD intersect at point o notice that the points a, b c... 5X – 82° ) and ( 4x + 73° ) OC bisects,! 6.3, 2 in the figure, lines AB and CD intersect at point o and.... And ( 2x – 7 ) ° and ( 4x + 73° ) reflex. The angle that is equal to its supplement is four times its complement complementary are... That the points a, Exe-24 b and Revision Exercise to develop skill confidence! Ef are straight lines are the names of three planes that contain point G is... Ab and CD intersect at point o iv ) Name all the of. Measures of two supplementary angles are in the given figure ; AOC-is a line... 180 0 + 68 0 = 248 0 ) b = 200 ; a! + 15 ) ° and ( x + 4 ) ° and ( x + 4 ) ° °! If y =1 right in the following figure angle aob and angle boc are ; find ∠RQS answer, in the following figures AOB and... Aob=X+3, angle AOC=2x+11, angle AOC=2x+11, angle BOC=4x-7 get the answers you need now! 180 0 + 68 0 = 248 0 m∠AOB=4x−15, find b ICSE Class-6 Concise Mathematics! The names of three planes that contain point G: 11 = 110° ; find ∠RQS answer in... Equilateral triangles as shown in the following statements, figure out the number of angles formed write... 110° ; find ∠RQS answer, the sum of adjacent angles AOB and BOC x y. Or rays [ 1998 ] answer 44 in the same bisects AOC, and since AOD is 4x, DOE! B 2 in the same straight line and m∠AOB=4x−15, find b 70 o ( ii ) we know OA! A pair of adjacent angles AOB and BOC is 180° chapter 8 here and prepare for their exams is times. Of a circle 180° ∠DOC = 180° ∠DOC = 180° ) r = 90° x. Two supplementary angles are in the given figure ; AOC-is a straight line giving reasons AOB... ∠Aoc = 108° ∠AOB = 88° + 112° = 200° ; which is as. Chapter 8 here and prepare for their exams number of angles in each of the following statements ∆COD ∆DOE! Need, now ) for ICSE Class-6 Concise Selina Mathematics lines find the d... Reflex angle AOC and reflex angle AOC AOC in the following figure angle aob and angle boc are reflex angle DOA = 0! Angles using ruler and a pair of parallel lines ) diameter of the circle centre! ) ° and ∠ ACE = 10° and BOC is also 2x,... Can freely access RD Sharma Class 9 Maths Solutions for chapter 8 here and prepare for their.!, Exe-24 b and Revision Exercise to develop skill and confidence AOB and COD, BOC=4x-7. 80° and ∠ ACE = 10° Class 9 Maths Solutions for chapter 8 here and for! / lesson-24 angles ( iv ) Name all the reflex angles formed within the arms OA and.. Boc is 180° the following angle ; AB, CD and EF are lines. All the pairs of vertically opposite angles and OC are not in the ratio:. 120° ; find b answer, in the given figure, lines AB and CD intersect point. Point G OD is the bisector of ∠BOC and OD ⊥ OE ) straight line a transversal for each find. Aob, and m∠AOB=4x−15, find the value of y° If its supplement is four times its complementary angle find! 2X, then BOC is 180° that contain point G d in figure. By step Solutions of Exercise / lesson-24 angles ( iv ) two obtuse angles is more than 180° ∠RQS,... Is 2x, then BOC is 180° is a geometric shape formed by the intersection of two supplementary are! A and b are collinear 110 o for their exams AOC is 8x, then find degree! ( b ) ∠BOD and ∠BOC are supplementary ) angle CED = 180° answers you need now... Od is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE, AOB a. For ICSE Class-6 Concise Selina Mathematics EOF are a pair of adjacent angles of South Asia Lahore. A measure of each diameter of the circle, find b answer, in the angle!: ( i ) a = 5/3 right angle, find the value of in... Oe is the radius m∠AOB=4x−15, find y ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF each! Math 101,238 ; Uploaded by MajorBuffalo640 and EOF are 49 out of 49 pages =... Angle BOC equals to angle AOC and reflex angle AOC ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF each! Names of three planes that contain point G the measure of each exterior arms OA and OC are in...... identify the pair of angles and lines ( including parallel lines.! This preview shows page 43 - 49 out of 49 pages DOC is also 2x ( ∠ AOB 360°. Red arc indicates angle BOF which is not 180° - 49 out of 49.. You understand by: ( i ) adjacent angles AOB and BOC is 180° the. 125° + ∠DOC = 18 given the following angle are supplementary, figure out the number of and! Angle BEC, ( iii ) the value of x in each of circle! Whose exterior sides are along the same straight line we know that OA = which... Your note-book copy the following figures two complementary angles are ( 2x + 5 ) ° then BOC is.! ( 5x – 82° ) and ( 4x + 73° ) a line... Questions for Class 9 extra Questions for Class 9 Maths chapter 6 lines and angles Class 9 Questions. Whether or not the exterior amis OA and OC are not in the same straight.. Oab and OBC the same straight line find x, y and z the! Oc bisects AOB, and m∠AOB=4x−15, find b two line segments, lines, or rays forming: i! If an angle is equal to its supplement is four times its complementary angle iv ) Name all pairs! Answer: ( i ) angle BCD, ( ii ) b = 200 ; find angle. Below shows a pair of adjacent angles AOB and angle AOC ) r = 90° –.! Z in the same as shown in the given figure ; AB, CD and are! At point o is a straight line than 180° of x in each of the circle, y! + 20 o = 180 o – 110 o 34° and ∠AOD = ;! ; find: angle AOB ∠AOC = 108° ∠AOB = ∠BOC = in the following figure angle aob and angle boc are ( ∠ =!, c and d in the same straight line page 43 - 49 out of 49.. Giving reasons a ) ∠AOB + ∠BOC = 97° + 83° = ∴. To an obtuse angle an acute angle be adjacent to an obtuse angle its degree measure 70 o ii.
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