Page 1 Cbse-spot.blogspot.com 1 Class IX Chapter 6 â€“ Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find ? BOE and reflex ? COE. Answer: Question 2: Page 2 Cbse-spot.blogspot.com 1 Class IX Chapter 6 â€“ Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find ? BOE and reflex ? COE. Answer: Question 2: Cbse-spot.blogspot.com 2 Let the common ratio between a and b be x. a = 2x, and b = 3x XY is a straight line, rays OM and OP stand on it. XOM + MOP + POY = 180º b + a + POY = 180º 3x + 2x + 90º = 180º 5x = 90º x = 18º a = 2x = 2 × 18 = 36º b = 3x= 3 ×18 = 54º MN is a straight line. Ray OX stands on it. b + c = 180º (Linear Pair) 54º + c = 180º c = 180º - In the given figure, lines XY and MN intersect at O. If ? POY = and a : b = 2 : 3, find c . Answer: Page 3 Cbse-spot.blogspot.com 1 Class IX Chapter 6 â€“ Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find ? BOE and reflex ? COE. Answer: Question 2: Cbse-spot.blogspot.com 2 Let the common ratio between a and b be x. a = 2x, and b = 3x XY is a straight line, rays OM and OP stand on it. XOM + MOP + POY = 180º b + a + POY = 180º 3x + 2x + 90º = 180º 5x = 90º x = 18º a = 2x = 2 × 18 = 36º b = 3x= 3 ×18 = 54º MN is a straight line. Ray OX stands on it. b + c = 180º (Linear Pair) 54º + c = 180º c = 180º - In the given figure, lines XY and MN intersect at O. If ? POY = and a : b = 2 : 3, find c . Answer: Cbse-spot.blogspot.com 3 54º = 126º c = 126º Question 3: In the given figure, PQR = PRQ, then prove that PQS = PRT. Answer: In the given figure, ST is a straight line and ray QP stands on it. PQS + PQR = 180º (Linear Pair) PQR = 180º - PQS (1) PRT + PRQ = 180º (Linear Pair) PRQ = 180º - PRT (2) It is given that PQR = PRQ. Equating equations (1) and (2), we obtain 180º - PQS = 180 - PRT PQS = PRT Page 4 Cbse-spot.blogspot.com 1 Class IX Chapter 6 â€“ Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find ? BOE and reflex ? COE. Answer: Question 2: Cbse-spot.blogspot.com 2 Let the common ratio between a and b be x. a = 2x, and b = 3x XY is a straight line, rays OM and OP stand on it. XOM + MOP + POY = 180º b + a + POY = 180º 3x + 2x + 90º = 180º 5x = 90º x = 18º a = 2x = 2 × 18 = 36º b = 3x= 3 ×18 = 54º MN is a straight line. Ray OX stands on it. b + c = 180º (Linear Pair) 54º + c = 180º c = 180º - In the given figure, lines XY and MN intersect at O. If ? POY = and a : b = 2 : 3, find c . Answer: Cbse-spot.blogspot.com 3 54º = 126º c = 126º Question 3: In the given figure, PQR = PRQ, then prove that PQS = PRT. Answer: In the given figure, ST is a straight line and ray QP stands on it. PQS + PQR = 180º (Linear Pair) PQR = 180º - PQS (1) PRT + PRQ = 180º (Linear Pair) PRQ = 180º - PRT (2) It is given that PQR = PRQ. Equating equations (1) and (2), we obtain 180º - PQS = 180 - PRT PQS = PRT Cbse-spot.blogspot.com 4 then prove that AOB is a line. = 360º (Complete angle) It is given that, x + y = z + w x + y + x + y = 360º 2(x + y) = 360º x + y = 180º Since x and y form a linear pair, AOB is a line. Question 5: In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that It can be observed that, x + y + z + w Question 4: In the given figure, if Answer: Page 5 Cbse-spot.blogspot.com 1 Class IX Chapter 6 â€“ Lines and Angles Maths Exercise 6.1 Question 1: In the given figure, lines AB and CD intersect at O. If and find ? BOE and reflex ? COE. Answer: Question 2: Cbse-spot.blogspot.com 2 Let the common ratio between a and b be x. a = 2x, and b = 3x XY is a straight line, rays OM and OP stand on it. XOM + MOP + POY = 180º b + a + POY = 180º 3x + 2x + 90º = 180º 5x = 90º x = 18º a = 2x = 2 × 18 = 36º b = 3x= 3 ×18 = 54º MN is a straight line. Ray OX stands on it. b + c = 180º (Linear Pair) 54º + c = 180º c = 180º - In the given figure, lines XY and MN intersect at O. If ? POY = and a : b = 2 : 3, find c . Answer: Cbse-spot.blogspot.com 3 54º = 126º c = 126º Question 3: In the given figure, PQR = PRQ, then prove that PQS = PRT. Answer: In the given figure, ST is a straight line and ray QP stands on it. PQS + PQR = 180º (Linear Pair) PQR = 180º - PQS (1) PRT + PRQ = 180º (Linear Pair) PRQ = 180º - PRT (2) It is given that PQR = PRQ. Equating equations (1) and (2), we obtain 180º - PQS = 180 - PRT PQS = PRT Cbse-spot.blogspot.com 4 then prove that AOB is a line. = 360º (Complete angle) It is given that, x + y = z + w x + y + x + y = 360º 2(x + y) = 360º x + y = 180º Since x and y form a linear pair, AOB is a line. Question 5: In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that It can be observed that, x + y + z + w Question 4: In the given figure, if Answer: Cbse-spot.blogspot.com 5 POR = 90º POS + SOR = 90º ROS = 90º - POS â€¦ (1) QOR = 90º (As OR PQ) QOS - ROS = 90º ROS = QOS - 90º â€¦ (2) On adding equations (1) and (2), we obtain ROS = QOS - POS 2 ROS = QOS - POS) ( Question 6: It is given that XYZ = and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ZYP, find XYQ and reflex QYP. Answer: It is given that OR PQ Answer: ?Read More

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