Question

why is (angle wxy) a right angle?
a (mangle wxy=2(mwidehat{wzy}))
(mangle wxy=90^{circ})
b (mangle wxy=mwidehat{wzy})
(mangle wxy = 180^{circ})
c (mangle wxy=90^{circ})

Explanation:

Step1: Recall the inscribed - angle theorem

The measure of an inscribed angle in a circle is half the measure of its intercepted arc. That is, if \(\angle WXY\) is an inscribed angle and \(\overset{\frown}{WZY}\) is the intercepted arc, then \(m\angle WXY=\frac{1}{2}m\overset{\frown}{WZY}\).

Step2: Consider the case of a semic - circle

Since \(WY\) is a diameter of the circle, the arc \(\overset{\frown}{WZY}\) is a semic - circle. The measure of a semic - circle is \(180^{\circ}\).
Substitute \(m\overset{\frown}{WZY} = 180^{\circ}\) into the formula \(m\angle WXY=\frac{1}{2}m\overset{\frown}{WZY}\).
We get \(m\angle WXY=\frac{1}{2}\times180^{\circ}=90^{\circ}\)

Answer:

C. \(m\angle WXY = 90^{\circ}\)