Question

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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Answer 1

Answer:

• C = 126°

Step-by-step explanation:

Given:-

• Lines XY and MN intersect at O.
• ∠POY = 90°

To Find:-

• C

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.

According to the question:-

→ ∠XOM + ∠MOP + ∠POY = 180º

→ b + a + ∠POY = 180º

→ 3x + 2x + 90º = 180º

→ 5x = 90º

→ x = 18º

Therefore,

• a = 2x = 2 × 18 = 36°

• b = 3x= 3 ×18 = 54°

MN is a straight line. Ray OX stands on it.

→ b + c = 180º (Linear Pair)

→ 54º + c = 180º

→ c = 180º − 54º = 126º

∴ c = 126º

Hence,

• C = 126°