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Given circle Q, PS is perpendicular to SR. If the measure of angle P is 36°, what is the measure of the arc SR in circle Q?

a) 36°
b) 72°
c) 108°
d) 144°

1 Answer

6 votes

Final answer:

To find the measure of arc SR intercepted by angle P, which is 36°, in circle Q, we double the angle's measure since an inscribed angle is half the measure of its intercepted arc. Thus, arc SR measures 72°. Therefore, the correct option is b.

Step-by-step explanation:

The problem involves finding the measure of an arc in a circle given the measure of an inscribed angle. The key relationship between an inscribed angle and its intercepted arc in a circle is that the inscribed angle is exactly half the measure of the intercepted arc. This is a fundamental concept in circle geometry.

Since the measure of angle P is given as 36° and angle P is an inscribed angle that intercepts arc SR, we can determine the measure of arc SR by doubling the measure of angle P. The calculation is simply 36° × 2 = 72°. Therefore, the measure of the arc SR in circle Q is 72°, which corresponds to option b.

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