A,B and C are the three points on a circle such that $$\angle$$ABC = $$35^{0}$$ and $$\angle$$BAC = $$85^{0}$$. What is the angle (in degrees) subtended by arc AB at the center of the circle?

Given : $$\angle$$ABC = $$35^\circ$$ and $$\angle$$BAC = $$85^\circ$$

To find : $$\angle$$ AOB = ?

Solution : In triangle, ABC

=> $$\angle A+\angle B+\angle C=180^\circ$$

=> $$85^\circ+35^\circ+\angle C=180^\circ$$

=> $$\angle C=180^\circ-120^\circ=60^\circ$$

Now, angle subtended by an arc at the centre is double the angle subtended by it at any point on the circle.

=> $$\angle AOB=2\times\angle ACB$$

= $$2\times60^\circ=120^\circ$$

=> Ans - (D)