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FinnZ [79.3K]
2 years ago
7

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

Mathematics
2 answers:
seraphim [82]2 years ago
8 0

we know that

The <u>inscribed angle</u> 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

<u>the answer is the option A</u>

90\°


nata0808 [166]2 years ago
6 0

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.


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