In a quadrilateral ABCD, the bisectors of ∠A and ∠B

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In a quadrilateral ABCD, the bisectors of ∠A and ∠B meet at O. If ∠C = 70° and ∠D = 130°, then measure of ∠AOB is

1. 40°
2. 60°
3. 80°
4. 100°

Correct Option: D

On the basis of question we draw a figure of quadrilateral ABCD

Here , ∠C = 70° and ∠D = 130°
We know that , ∠A + ∠B + ∠C + ∠D = 360°
⇒ ∠A + ∠B + 70° + 130° = 360°
⇒ ∠A + ∠B = 360° – 70° – 130° = 160°
In ∆ AOB,
∠OAB + ∠OBA + ∠AOB = 180°

⇒	∠A	+	∠B	+ ∠AOB = 180°
	2		2

⇒	1	(∠A + ∠B) + ∠AOB = 180°
	2

⇒	1	× 160° + ∠AOB = 180°
	2

⇒ ∠AOB = 180° – 80° = 100°