Quadrilateral ABCD is inscribed in this circle. What is the measure of angle C?

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m∠C = 122°

Step-by-step explanation:

Opposite angles of a quadrilateral inscribed in a circle are supplementary. This means

m∠A + m∠C = 180°

m∠B + m∠D = 180°

To find angle C we need to find x, then subtract m∠A from 180°

x+20=3x

20=2x

x=10

Now we substitute 10 in for x

m∠A=2(10)+38

m∠A=20+38

m∠A=58°

Now we subtract this value from 180.

m∠C=180-58

m∠C=122°

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step-by-step explanation:

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