Question

A circle is shown. Points Q, U, A, D are on the circle. Lines connect the points to form a quadrilateral. Angle Q U A is 111 degrees. Arc Q U is 88 degrees.
What is the measure of Arc A U?

44°
50°
64°
92°

Answer 1

Inscribed angle QUA intercepts arc QA, so arc QA = 2·111° = 222°. The remaining arc from Q to A through U is 360° − 222° = 138°, and that equals arc QU + arc UA = 88° + arc AU. Thus arc AU = 138° − 88° = 50°.

Answer: 50°.