Question

Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle C?
Enter your answer in the box.

Answer 1

Answer: Angle C = 80

Explanation:

Here, Quadrilateral ABCD is inscribed in circle.

Angle A = 2x+4

Angle B = 2x-1

Angle D = 3x-59

Quadrilateral ABCD is inscribed in circle.

Therefore,The Summation of opposite sides are supplementary and equal to 180.

Angle D + Angle B = 180

(3x-59) + (2x-1) = 180

5x - 60 = 180

5x = 240

x= 48

We know, Sum of all interior angle of Quadrilateral is 360

Angle A + Angle B + Angle C +Angle D = 360

(2x+4) + (2x-1) + Angle C + 3x-59= 360

7x - 56 + Angle C = 360

7x + Angle C = 416

Angle C = 416 - 7x

Angle C = 416 - 7×48

Angle C = 416 -336