In a circle, what is the measure of the central angle subtending the same arc as an inscribed angle of 30 degrees?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

In a circle, what is the measure of the central angle subtending the same arc as an inscribed angle of 30 degrees?

Explanation:
The central angle that subtends the same arc as an inscribed angle is twice the inscribed angle, because the inscribed angle measures half of the arc’s degree measure. If the inscribed angle is 30 degrees, the intercepted arc measures 60 degrees, so the central angle subtending that same arc must be 60 degrees. The other options would correspond to different relationships between central and inscribed angles that don’t match this arc, so they don’t fit. The central angle is 60 degrees.

The central angle that subtends the same arc as an inscribed angle is twice the inscribed angle, because the inscribed angle measures half of the arc’s degree measure. If the inscribed angle is 30 degrees, the intercepted arc measures 60 degrees, so the central angle subtending that same arc must be 60 degrees. The other options would correspond to different relationships between central and inscribed angles that don’t match this arc, so they don’t fit. The central angle is 60 degrees.

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