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

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

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In the figure, lines XY and MN

intersect at O and ∠ POY = 90°.

Also, given a : b = 2 : 3

Let a = 2x and b = 3x.

Since, ∠XOM + ∠POM + ∠POY = 180°

(Linear pair axiom)

⇒ 3x + 2x + 90° = 180°

⇒ 5x = 180° – 90°

⇒ x = 90 5 ° = 18°

∴ ∠XOM = b = 3x = 3 × 18° = 54°

and ∠POM = a = 2x = 2 × 18° = 36°

Now, ∠XON = c = ∠MOY = ∠POM + ∠POY

(Vertically opposite angles)

= 36° + 90° = 126°

Hence, c = 126° Ans.