In quadrilateral ABCD, ∠C = 72°, ∠D = 28°. The bisectors of ∠A and ∠B meet in O. What is the measure of the ∠AOB?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 50°
Angle sum of the quadrilateral = 360°
∠A + ∠B + ∠C + ∠D = 360°
⇒ ∠A + ∠B + 100º = 360°
⇒ ∠A + ∠B = 260°
Now,
In ΔAOB:
(∠A/2) + (∠B/2) + ∠AOB = 180°
⇒ [(∠A + ∠B)/2] + ∠AOB = 180°
⇒ (260/2) + ∠AOB = 180°
⇒ ∠AOB = 180° - 130° = 50°