Question

​Quadrilateral ABCD​ is inscribed in this circle.

What is the measure of angle C?
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Answer 1

The measure of angle C is 92°

Explanation:

In a quadrilateral opposite angles are supplementary (Angles add up to 180°)

So since we have two opposite angles already set up the equation:

(x+24)+(x+10) = 180

Combine like terms - x+x+24+10 = 180 → 2x+34 = 180

Cancel out the constant to solve for x: 2x+34-34 = 180-34

Divide both sides by 2 so x is isolated: 2x/2=146/2

Solve: x=73

Now that we know x = 73 we can find angle C by setting up the equation:

Let C represent the unknown angle of ∠C

73+15+C=180

Combine like terms: 88+C=180

Isolate C: 88-88+y=180-88

Solve for C: C=92