If an inscribed angle measures 45 degrees, what is the measure of the central angle subtending the same arc?

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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

If an inscribed angle measures 45 degrees, what is the measure of the central angle subtending the same arc?

Explanation:
In a circle, an inscribed angle intercepts an arc and has a measure equal to half the arc’s measure, while a central angle subtending that same arc measures the arc itself. So the central angle is twice the inscribed angle. If the inscribed angle is 45 degrees, the intercepted arc measures 90 degrees, and the central angle subtending that arc is 90 degrees.

In a circle, an inscribed angle intercepts an arc and has a measure equal to half the arc’s measure, while a central angle subtending that same arc measures the arc itself. So the central angle is twice the inscribed angle. If the inscribed angle is 45 degrees, the intercepted arc measures 90 degrees, and the central angle subtending that arc is 90 degrees.

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