Question

A student inscribes a triangle within a semicircle. What is the measure of ∠XYZ?

a. 90°
b. 60°
c. 45°
d. 120°

Answer 1

we know that

The inscribed angle measures half that of the arc that comprises

In this problem

∠XYZ------> is the inscribed angle

∠XYZ=$\frac{1}{2}[arc\ XZ]$

$arc\ XZ=180\°$ ------> because is a diameter of the circle

substitute

∠XYZ=$\frac{1}{2}[180\°]=90\°$

therefore

the answer is the option A

$90\°$

Answer 2

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.