In the given figure, lines XY and MN intersect at O. If ∠POY = 90° and a:b = 2 : 3, find c. - Mathematics

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In the given figure, lines XY and MN intersect at O. If ∠POY = 90° and a:b = 2 : 3, find c.

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Solution

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 − 54º = 126º

∴ c = 126º

Concept: Pairs of Angles
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Chapter 6: Lines and Angles - Exercise 6.1 [Page 97]

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NCERT Mathematics Class 9
Chapter 6 Lines and Angles
Exercise 6.1 | Q 2 | Page 97

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