Question

AB is the diameter of a circle with centre O.

The value of y is ___

• A. ${110}^{\circ }$
• B. ${120}^{\circ }$
• C. ${60}^{\circ }$
• D. ${150}^{\circ }$

Answer 1

The correct option is B

${120}^{\circ }$

OC = OB (radis of the circle)

So, $x={60}^{\circ }$ ($\Delta OCB$ is an isosceles triangle)

So, $\angle COB+60+x={180}^{\circ }$
(Sum of angles of a triangle)

$\angle COB=180-120={60}^{\circ }$

Now,

$y+\angle COB=180$ (angles on a straight line )

$y+60={180}^{\circ }$

$y={120}^{\circ }$