Question

For the given figure, P is the center of the circle.
Find the ∠XWZ.


degrees

Answer 1

The side XY passes through the center of the circle and touches the circle at both ends.
Hence, it is the diameter of the circle.

The angle subtended by the diameter to any point on the circle is equal to ${90}^o.$
$\therefore \angle XZY={90}^o,$ and $△XYZ$ is a right triangle.

Similarly for $△XYW$,
$\angle XWY={90}^o.$

For $△XYZ,$
$\angle YXZ={180}^o-{90}^o-{35}^o={55}^o$

We know that the measure of all angles subtended by an arc on the rest part of circumference of the circle are equal.

Considering the minor arc ZY,
$\angle ZWY=\angle ZXY={55}^o$

$\angle XWY=\angle XWZ+\angle ZWY$
$\Rightarrow {90}^o=$\angle XWZ+55^o\Rightarrow $\angle XWZ={90}^o-{55}^o={35}^o$