Question

) In a figure given below, lines AB and PQ intersect at O if AON=90° and PON=60°, then find
AOQ.
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Answer 1

Answer:

Step-by-step explanation:

In the fig., lines PQ, MN and RS are intersecting each other at o

X : y = 1 : 2 , z = 90°

∠MOQ = ∠PON = z

(Vertically opposite angle

Now, RS is a straight line

∴ x + z + y = 180°

⇒ x + y + 90° = 180° (∵ z = 90°)

⇒ x + y = 180° - 90° = 90°

But x : y = 1 : 2

Let x = a then y = 2a

∴ a + 2a = 90°

⇒ 3a = 90°

⇒ a = 90°/3 = 30°

∴ x = 30° and y = 2a = 2 × 30° = 60°

Now, ∠ ROM = y = 60°

And ∠ POR = ∠SOQ

(Vertically opposite angles)

= x = 30°