If the central angle subtending arc AB is 80 degrees, what is the measure of the inscribed angle subtending the same arc?

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Multiple Choice

If the central angle subtending arc AB is 80 degrees, what is the measure of the inscribed angle subtending the same arc?

In a circle, an inscribed angle is half the measure of its intercepted arc, while a central angle subtending the same arc equals the arc’s measure. Here, the central angle subtending arc AB is 80 degrees, so arc AB measures 80 degrees. An inscribed angle that subtends the same arc AB intercepts that 80-degree arc, so its measure is half of 80, which is 40 degrees. Therefore the inscribed angle is 40 degrees.

In a circle, an inscribed angle is half the measure of its intercepted arc, while a central angle subtending the same arc equals the arc’s measure. Here, the central angle subtending arc AB is 80 degrees, so arc AB measures 80 degrees. An inscribed angle that subtends the same arc AB intercepts that 80-degree arc, so its measure is half of 80, which is 40 degrees. Therefore the inscribed angle is 40 degrees.

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