Question

The circle below has center Z. Suppose that m XY = 122°. Find the following.

Answer 1

Answer:

m∠XZY = 122°

m∠XWY = 61°

Step-by-step explanation:

From the picture attached,

A circle has been given with center as Z.

∠XZY is a central angles subtended by the arc XY,

Therefore, measure of angle XZY will be equal to measure of ∠XZY.

m(∠XZY) = m(arc XY) = 122°

By another property of the circle,

"Inscribed angle measures the half of the central angle intercepted by the same arc."

Therefore, m∠XWY = $\frac{1}{2}(\angle XZY)$

                                 = $\frac{1}{2}(122)$

                                 = 61°