Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle C?

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°

A quadrilateral inscribed in a circle. The vertices of the quadrilateral lie on the edge of the circle and are labeled as A, B, C, D. The interior angle A is labeled as left parenthesis 2 x plus 3 right parenthesis degrees. The angle B is labeled as left parenthesis 2 x minus 4 right parenthesis degrees. The angle D is labeled as left parenthesis 3 x plus 9 right parenthesis degrees.

The measure of angle C is 107°

Explanation:

Given that ABCD is a quadrilateral.

The vertices A, B, C, D lie on the edge of the circle.

The measure of angle A is

The measure of angle B is

The measure of angle D is

We need to determine the measure of angle C

Since, we know that the opposite angles B and D are supplementary.

Thus, we have,

Substituting the values, we get,

Thus, the value of x is 35

Substituting the value of x in the measures of angles A, B and D, we get,

Similarly,

For angle D, we have,

Now, we shall find the measure of angle C

Since, we know that all the angles in a quadrilateral add up to 360°

Thus, we have,

Substituting the values of A, B and D, we get,

Thus, the measure of angle C is 107°

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