Middle School

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GD is a diameter of circle C.

Circle C is shown. Line segments CF, CG, CA, CB, CD, and CE are radii. Angle GCF is 51 degrees, angle FCE is 90 degrees, and angle DCE is 39 degrees.

What is the measure of arc GEB?

A. 90°
B. 180°
C. 219°
D. 231°

Answer :

Applying the central angle theorem of a circle, the measure of arc CEB is same as the measure of angle GCB = 231°.

What is the Central Angle Theorem?

Based on the central angle theorem, it states that the measure of an intercepted arc equals the measure of its central angle.

Here, By figure;

Measure of arc GEB = measure of angle GCB

Here, We get;

⇒ m ∠GCB = 51 + 90 + 39 + 51

⇒ m ∠GCB = 231°

Hence, Measure of arc GEB = 231°

Learn more about central angle theorem on:

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Rewritten by : Jeany