Question

Use the image to answer the question.

Quadrilateral upper Q upper U upper A upper D is drawn within a circle such that all vertices touch the edge of the circle.

In the diagram, the following measures are given: m∠A=93°
, mAU=126°
, and mQU=90°
. Find the m∠U
.

(1 point)
m∠U=
º

Answer 1

m∠U = 1/2 · m(arc QA). Arc QA = 360° − (arc QU + arc AU) = 360° − (90° + 126°) = 144°.
So m∠U = 1/2 · 144° = 72°.