Question

Find the value of x + y in the figure given below:

• A. ${70}^{\circ }$
• B. ${90}^{\circ }$
• C. ${75}^{\circ }$
• D. ${62}^{\circ }$

Answer 1

The correct option is B

${90}^{\circ }$

$\angle OBA=y$

Since, OA = OB (radius of the circle)

So, $\angle OAB=\angle OBA=y$

So, $y+y+z={180}^{\circ }$

$z+2y={180}^{\circ }$

Now, $z=2x$

(As angle subended by an arc at the centre is twice the angle subtended by the same arc at the circumference )

So, $2x+2y={180}^{\circ }$

$x+y={90}^{\circ }$