Question

In the given figure AB is the diameter of the circle. Find the value of y.

• A. ${40}^{\circ }$
• B. ${90}^{\circ }$
• C. ${50}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${40}^{\circ }$

We know that the angle in a semicircle is a right angle.
$\therefore \angle ACB=x={90}^{\circ }$
Using angle sum property in $△ABC,$ we have
$\angle ABC+\angle ACB+\angle CAB={180}^{\circ }.$
i.e.,$y+{90}^{\circ }+{50}^{\circ }={180}^{\circ }$
$⟹y={180}^{\circ }-{140}^{\circ }={40}^{\circ }$