(ii) angle EOD (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. School University of South Asia, Lahore - Campus 1; Course Title MATH 101,238; Uploaded By MajorBuffalo640. Solution: No, the sum of the measures of two obtuse angles is more than 180°. Each figure given below shows a pair of adjacent angles AOB and BOC. Angles ICSE Class-6th Concise Selina Maths Solutions Chapter-24 (With their Types) . In the figure, OD is the bisector of ∠AOC, OE is the bisector of ∠BOC and OD ⊥ OE. ... Identify the property, definition, postulate or theorem that justifies the following statements. Can two adjacent angles be complementary? supplementary 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. The diagram is not to scale. Find the value of x. Question 4: If O is the centre of the circle, find the value of x in each of the following figures. In the given figure ; AOC-is a straight line. If angle AOB = 28, Angle BOC = 3X-2, and Angle AOD = 6x... and if Angle AOD = a total of 110 degrees. Answer, Explain what do you understand by : (i) ∠SQR = 75° ; find ∠PQS. Using the angle sum property ∠AOB + ∠OAB + ∠OBA = 180 o. We want to find angle AOB ∠AOC = 108° ∠AOB = 3x+4 ∠BOC =8x−28 Check attachment for understanding. Answer, Two supplementary angles are in the ratio 7 : 11. (ii) the complement and the supplement of the angle obtained above. (iii) 9 O’clock (i) 49° What are the names of three planes that contain point G? In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° . Answer: (d) none of these. (ii) ∠PQS = 110°; find ∠RQS (ii) b = 200 ; find a. Identify the pair of angles in each of the figure given below . Answer, Find the angle formed by the arms of a clock at: Identify the property, definition, postulate or theorem that justifies the following statements. 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. (iii) (x – 10)° (ii) ∠BQP = …….. find : angles COD and BOD. (ii) ∠AOB + ∠BOC = 97° + 83° = 180° ⇒ The sum of adjacent angles AOB and BOC is 180°. (ii) in the exterior of the angle PQR. (i) 29° 16′ 23″ and 8° 27′ 12″ 11x — 24 = 108. (iii) ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. 10. Given the following angle . [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. Also ∠AOB + ∠BOC = 180° ∴ ∠AOB and ∠BOC are supplementary. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of : If the ray in the middle creates two equal angles, ... then m∠AOB + m∠BOC … An angle is a geometric shape formed by the intersection of two line segments, lines, or rays. ∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°. 13. (iv) The reflex angles in the given figure are, ∠BOC and ∠DOA, Reflex angle BOC = 180 0 + 68 0 = 248 0. 29. 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. In the following figure, ∠ AOB and ∠ BOC are (a) complementary angles (b) supplementary angles (c) adjacent angles (d) none of these. The red arc indicates angle BOF which is given as 120°. complementary angles. (iii) ∠AQR = ……. 8. Answer, In the given figure, PQR is a straight line. Answer, In the given figure if : (iv) 20° + y° a b 2 In the following figures AOB COD and EOF are straight lines Find the. In the given Fig 5.10, are the following adjacent angles? Since OE bisects AOD, and since AOE is 2x, then DOE is also 2x. (ii) two acute angles, (iii) two obtuse angles 2. Explain your answer. 11x = 108 + 24. ⇒ The exterior amis OA and OC are not in the same straight line. ∠GQL c. ∠MQK d. ∠IQH 9. If m∠AOC=85°, m∠BOC=2x+10, and m∠AOB=4x−15, find the degree measure of ∠BOCand∠AOB. Answer, For an angle y°, find : Lines and Angles Class 9 Extra Questions Very Short Answer Type. Find whether or not the exterior arms OA and OC are in the same straight line. 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. Angle ∠ AOB = 80° and ∠ ACE = 10°. OA and OC are in the same straight line. (iii) Name all the pairs of adjacent angles. (3 marks) (c) Are the areas of OAB and OBC the same? 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. (iii) obtuse angle BOD (∠ AOB + ∠ BOC = 180°) r = 90° – x. Can two obtuse angles be adjacent angles? (i) If x = 53°, find y. Can an acute angle be adjacent to an obtuse angle? (i) angle BOC (ii) x° (ii) its complementary angle. (ii) the supplementary angle then ∠CDB is a right angle. (i) 45° Question 1. Explain your answer. Answer, Find the angle : Answer, The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. (i) 3 O’clock In parts (a) and (b) of the following, relationships among marked angles are given below the figure. (iii) the value of x° if its supplementary angle is three times its complementary angle. none of these. Calculate: (i) Angle BEC, (ii) Angle BCD, (iii) Angle CED. Answer, Write the complement angle of : ∠DFG and ∠JKL are complementary angles. Then what is the measurement of Angle BOC and Angle AOD (iii)∠COB + ∠AOB = 88° + 112° = 200° ; which is not 180°.⇒ The exterior amis OA and OC are not in the same straight line. Can two adjacent angles be supplementary? = 90° – Question 44. The base angles of an isosceles triangle are equal. 3. So we get ∠BOC = 70 o (ii) We know that OA = OB which is the radius. Each figure given below shows a pair of parallel lines cut by a transversal For each case find a and b giving reasons. 30. ∠BOC + ∠DOC = 180° 125° + ∠DOC = 180° ∠DOC = 18 Reflex angle DOA = 180 0 + 68 0 = 248 0. (iv) 47° and 61° 17’4″ adjacent angles. For triangles AOB and COD, angle … (i) three pairs of adjacent angles. Answer, In the given figure; AB, CD and EF are straight lines. Question 29. 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°. This preview shows page 43 - 49 out of 49 pages. Solution: Yes, In the figure ∠AOB and ∠BOC are adjacent angles. From the attachment, we notice that the sum of angle AOB and angle BOC equals to angle AOC. (m) 56° 38′ and 27° 42’30” Which of the following statements is false? Answer, Find the angle that is three times its complementary angle. Find the value ofx and also answer each of the following : Find the angles. Name an angle supplementary to ∠MQI. Answer, In the given figure ; PQR is a straight line. If an angle is half of its complementary angle, then find its degree measure. Answer. Can two obtuse angles form a linear pair? (i) its supplementary angle. Find the measure of the marked angles. (i) ∠AQB = …….. (iv) Name all the reflex angles formed and write the measure of each. (iii) Supplementary 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. Theorem 1: Prove that the sum of all the angles formed on … Answer, In the given figure, figure out the number of angles formed within the arms OA and OE. Answer, Two supplementary angles are in the ratio 7 : 5. Answer, In the given figure : (iii) a = 5/3 right angle, find b (iv) which angle is acute ? (iv) 12 O’clock By substituting the values ∠AOB + 20 o + 20 o = 180 o. find : angle AOB and angle AOC. (ii) Complementary angles ? 3x + 8x + 4—28 = 108. Again, by degree measure theorem ∠BOC = … Answer. 11. (ii) 111° In the following figure, reflex ∠ AOB is equal to (a) 60° (b) 120° (c) 300° (d) 360° Answer/Explanation. Pages 49. (iii) (x – 30)° Extra Questions for Class 9 Maths Chapter 6 Lines and Angles with Solutions Answers. Answer, Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles. Answer, Add : (iv) 20° + y° (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. (i) ∠AOP = …….. THINK, DISCUSS AND WRITE 1. (iii) which angle is obtuse ? ⇒ The sum of adjacent angles AOB and BOC is 180°. ∠AOB + ∠BOC = ∠AOC. An angle can also be thought of as a fraction of a circle. Find x. Since, the sum of adjacent angles AOB and COB = 180°. Since ∆AOB, ∆BOC, ∆COD, ∆DOE, ∆EOF ∴ Each angle is equal to 60°. We provide step by step Solutions of Exercise / lesson-24 Angles (With their Types) for ICSE Class-6 Concise Selina Mathematics. In your note-book copy the following angles using ruler and a pair compass only. Find x, y and z in the figure given below . Our Solutions contain all type Questions of Exe-24 A, Exe-24 B and Revision Exercise to develop skill and confidence. In each case given below draw perpendicular to AB from an exterior point P. In AOB. Can two adjacent angles be supplementary? find : reflex angle AOC and reflex angle AOD. Answer, In the given figure, lines AB and CD intersect at point O. A b 2 in the following figures aob cod and eof are. properties of angles and lines (including parallel lines). 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. (i) in the interior of the angle PQR, In figure, if x + y = w + z, then prove that AOB … ∠IQG b. (v) reflex angle COE. Answer, Two supplementary angles are (5x – 82°) and (4x + 73°). (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. Ex 6.3, 2 In figure, ΔODC ∼ ΔOBA, ∠BOC = 125° and ∠CDO = 70°. 3x + 4 + 8x —28 = 108. Since OD bisects AOC, and since AOD is 4x, then DOC is also 4x. (ii) vertically opposite angles. a. Answer, Two complementary angles are in the ratio 8 : 7. Question 2. (i) the complementary angle Find the angles. (ii) that is equal to its supplement ? Answer, Use the adjoining figure to find : (i) the angle Answer, The measures of two complementary angles are (2x – 7)° and (x + 4)°. (iv) reflex angle BOD (ii) 9° 45’56” and 73° 8′ 15″ (i) ∠BOD [1998] Answer 44 If : 12. Find the value of ‘x’ for each of the following figures : Find ∠DOC, ∠DCO and ∠OAB. Name the pair of angles forming : Then complete the following: 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. Angles are a measure of rotational distance as contrasted with linear distance. Therefore, we have six equilateral triangles as shown in the figure. (ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ; (ii) Name all the pairs of vertically opposite angles. (iii) the value of y° if its supplement is four times its complement. (i) Adjacent angles ? ∠BOC = 180 o – 110 o. Find the angles. OA and OC are in the same straight line. Answer, Name the points : In part (c), find only the measure of BOC and tell why the exact values of x and y cannot be determined. In the given figure, AC is the diameter of the circle with centre O. CD and BE are parallel. Answer, In the given figure, AOB is a straight line. ⇒ The exterior amis OA and OC are not in the same straight line. (i) that is equal to its complement ? Therefore Angle FOG = Angle COG. Answer, In the given diagram, ABC is a straight line. (ii) 6 O’clock (ii) ∠BOP = …….. (i) Find the value of ∠a. 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. Answer, For an angle x°, find : Since OC bisects AOB, and since AOC is 8x, then BOC is also 8x. 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) straight line angles. Angle AOB=x+3, angle AOC=2x+11, angle BOC=4x-7 Get the answers you need, now! A O C. Find a, b, c and d in the figure given below . 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 … Question 3. Answer, Write the supplement angle of : Since OF bisects AOE, we let AOF and FOE be x degrees each. 4. asked Jan 31, 2018 in … (Leave the answer in surd from.) Answer, In the figure, given below name : Name four rays shown. ∠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. Show that the points A, 0 and B are collinear. (4 marks) (b) Find the area of ABC. In the given figure ; AOC-is a straight line. (a) ∠AOB and ∠BOC (b) ∠BOD and ∠BOC Justify your answer . Answer: (c) Explanation : ∠ AOB = 360° – 60° = 300°. (iii) If ∠AOB = ∠BOC = ∠COD = 38° (ii) ∠AOC So we get ∠OBA= ∠OAB = 20 o. (ii) If y =1 right angles ; find x. Find x. (i) a = 130° ; find b. (iv) two reflex angles. The exterior arms. Answer Definition of perpendicular lines. 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. Each figure given below shows a pair of adjacent angles AOB and BOC. ∴ The exterior arms OA and OC are in the same straight line. Find x. The given diagram shows two adjacent angles AOB and AOC whose exterior sides are along the same straight line. Find the angles. (i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°; In the following figure, ∠AOB and ∠BOC are. Answer, An angle is one-thirds of a straight line angle ; find : Answer, In the given figure ; AOC-is a straight line. ∴ The exterior arms OA and OC are in the same straight line. Students can freely access RD Sharma class 9 Maths solutions for chapter 8 here and prepare for their exams. 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, Following angle from the attachment, we notice that the sum of adjacent angles 75° ; ∠RQS. And angles with Solutions answers AOB is a straight line the answers you need,!. 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