Question

Determine the angle $\angle ZWY$ for P as center of the given circle.

• A. ${35}^o$
• B. ${45}^o$
• C. ${55}^o$
• D. Insufficient data.

Answer 1

The correct option is C ${55}^o$

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 ${90}^o.$
$\therefore \angle Z={90}^o,$ and the given triangle is a right triangle.

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

We know that the measure of all angles subtended by an arc on the same segment of the circle are equal.

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