The measure of <C is 38°. The answer is the first option 38°
Circle theorems
From the question, we are to determine the measure of <C.
In the diagram, <C is an angle on a part of the circumference.
From the given information, the angle subtended by arc AB at the center of the circle is 76°
From one of the circle theorems we have that
The angle subtended by an arc of a circle at its center is twice the angle it subtends anywhere on the circle's circumference
Therefore,
2 × <C = 78°
<C = 76° ÷ 2
<C = 38°
Hence, the measure of <C is 38°. The answer is the first option 38°
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