Question

m\overarc{xz}=67^{\circ}
\angle xyz=________\circ

Explanation:

Step1: Apply the inscribed angle theorem

The measure of an inscribed angle is half the measure of its intercepted arc.
$$\angle XYZ=\frac{1}{2}\text{m}\widehat{XZ}$$

Step2: Substitute the given arc measure

Given \(\text{m}\widehat{XZ} = 67^{\circ}\), substitute into the formula.
$$\angle XYZ=\frac{1}{2}\times67^{\circ}$$

Step3: Calculate the angle measure

$$\angle XYZ = 33.5^{\circ}$$

Answer:

\(33.5\)