Question

HELP! 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

I don’t understand what you mean by the quadrilateral ABCD is inscribed in the circle below

Answer 2

Explanation:

If a quadrilateral is inscribed in a circle with all four edges touching the circumference of the circle, then the opposite angles are supplementary. This means that the sum of the opposite angles is 180 degrees. Therefore,

Angle B + angle D = 180

Angle A + angle C = 180

3x + x + 20 = 180

4x = 180 - 20 = 160

x = 160/4

x = 40

Angle A = 2 × 40 + 78 = 158 degrees

Angle B = 3 × 40 = 120 degrees

Angle C = 180 - 158 = 22 degrees

Angle D = 40 + 20 = 60 degrees