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प्रश्न
In the given figure, lines XY and MN intersect at O. If ∠POY = 90° and a : b = 2 : 3, find c.
उत्तर
∠POY = 90° (Given)
Let ∠a and ∠b = 2x and 3x.
Since XOY is a straight line.
So, ∠a + ∠b + ∠POY = 180° ...(Linear pair)
⇒ 2x + 3x + 90°= 180°
⇒ 5x = 180° − 90°
⇒ 5x = 90°
⇒ x = `(90°)/5`
⇒ x = 18°
Now, ∠a = 2 × 18°
= 36°
∠b = 3 × 18°
= 54°
Here, MON is also a straight line.
∠b + ∠c = 180° ...(Linear pair)
∠54° + ∠c = 180°
⇒ ∠c = 180° − 54°
∴ c = 126°
Thus, the required measure of c = 126°.
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