Question

The line passes through the center of the given circle. Find the angle ∠Y.

degrees

Answer 1

$△XYZ$ is a right triangle as the angle subtended by the diameter ZY to X on the circle is equal to ${90}^o.$

Hence, $\angle X={90}^o.$
Given: $\angle Z={31}^o$

Using the sum of interior angle property,
$\angle Z+\angle Y+\angle X={180}^o$
$\Rightarrow {31}^o+\angle Y+{90}^o={180}^o$
$\Rightarrow \angle Y={90}^o-{31}^o={59}^o$