Question

Quadrilateral ABCD is inscribed in a circle. Find the measure of angle D. Show your work.

Answer 1

80°

Explanation:

The opposite angles of an inscribed quadrilateral add up to 180.

(2x + 13) + (3x + 37) = 180

(2x + 3y) + (5y) = 180

Solving the first equation:

5x + 50 = 180

5x = 130

x = 26

Solving the second equation:

2x + 8y = 180

2(26) + 8y = 180

52 + 8y = 180

8y = 128

y = 16

5y = 80. So ∠D = 80°.