Question

A. In your own words, use 2-3 sentences to describe the special relationship between opposite angles when a quadrilateral is inscribed in a circle.

b. Quadrilateral ABCD is inscribed in the circle below.

Write an equation and solve for x.
Find the measure of all four angles. Find m⦨A, m⦨B, m⦨C, and m⦨D.
Explain your steps in solving the problem. Your explanation should include 2-3 sentences.

Answer 1

x = 40°

Angle A: 118°

Angle B: 120°

Angle C: 62°

Angle D: 60°

Explanation:

When a quadrilateral is inscribed inside a circle, opposite angles add up to 180.

(x + 20) + 3x = 180

4x + 20 = 180

4x = 160

x = 40°

Angle A: 2(40) + 38 = 118°

Angle B: 3(40) = 120°

Angle C: 180 - 118 = 62°

Angle D: 40 + 20 = 60°