Astudent inscribes a triangle within a semicircle. what is the measure of ∠xyz?

a. 90°
b. 60°
c. 45°
d. 120°

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=

⇒ ∠XYZ=

Since XZ is a diameter of the circle which is a line segment, thus ∠XZ=180°

∴ ∠XYZ=

∴ ∠XYZ=

Therefore, a. 90° is the measure of ∠XYZ.

we know that

The inscribed angle measures half that of the arc that comprises

In this problem

∠XYZ------> is the inscribed angle

∠XYZ=

------> because is a diameter of the circle

substitute

∠XYZ=

therefore

the answer is the option A

99

step-by-step explanation: