Answer: a. 90°
Step-by-step explanation:
We know that the in a circle, the measure of an inscribed angle is half the measure of the central angle with the same intercepted arc.
In the problem∠XYZ is the inscribed angle
∠XYZ=\(\frac{1}{2}\ arc(XZ)\)
⇒ ∠XYZ=\(\frac{1}{2}\angle{XZ}\)
Since XZ is a diameter of the circle which is a line segment, thus ∠XZ=180°
∴ ∠XYZ=\(\frac{1}{2}180^{\circ}=90^{\circ}\)
∴ ∠XYZ=\(90^{\circ}\)
Therefore, a. 90° is the measure of ∠XYZ.
