ErnieIrwin
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PLZ HELP!!! WILL GIVE BRAINLIEST ANSWER!

This figure shows circle O with inscribed ∠XYZ .

m∠XYZ=76∘



What is the measure of XYZ?

Enter your answer in the box.

PLZ HELP WILL GIVE BRAINLIEST ANSWER This figure shows circle O with inscribed XYZ mXYZ76 What is the measure of XYZ Enter your answer in the box class=

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Answer:
208°.

Explanation:
To find the measurement of arc XYZ, we must first find the measurement of the minor arc XZ and subtract that from the whole circle (360°).

We are given angle XYZ which is the information we need to find arc XZ.
Arc XZ is twice the size of angle XYZ because it is an inscribed angle.
This means that:
XZ=2XYZ.

Substitute the angle measurement.
XZ=2(76)=152°.

Subtract 152 from 360 to get the measurement of arc XYZ.
360-152= 208°

Answer:

[tex]\text{Measure of arc XYZ}=208^{\circ}[/tex]

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of arc XYZ.

Upon looking at our given circle we can see that angle XYZ is the inscribed angle of our given angle.

Since the measure of an inscribed angle is half the measure of its intercepted arc, so the measure of arc XZ will be two times the measure of angle XYZ.

[tex]m\angle XYZ=76^{\circ}[/tex]

[tex]\text{Measure of arc XZ}=2\times 76^{\circ}[/tex]

[tex]\text{Measure of arc XZ}=152^{\circ}[/tex]

Since all the arcs of a circle add up-to to 360 degrees, so the measure of arc XYZ will be 360 minus the measure of arc XZ.

[tex]\text{Measure of arc XYZ}=360^{\circ}-152^{\circ}[/tex]

[tex]\text{Measure of arc XYZ}=208^{\circ}[/tex]

Therefore, the measure of arc XYZ is 208 degrees.

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