Question

In the given figure, AB is diameter of the circle and O is the
centre. If the measure of angleCOB = 40°, then the measure of
angleCAB will be:
(a) 20°
(b) 30°
(c) 40°
(d) 60°​

Answer 1

The Angle CAB will be (a) 20°

As AB is a straight line,

Angle COB + COA = 180°

Therefore, Angle COA = 140°

In triangle OAC,

OA = OC (radius of the circle)

So Angle OAC = OCA

OAC = CAB (same angles)

Using sum of angles of a triangle,

Angle COA + OAC + OCA = 180°

140° + 2 OAC = 180°

OAC = CAB = 20°