Asked by logan

Circle U is shown. Chords R T and Q S intersect at a point forming 4 angles. The top left angle is angle 1, and the top right angle is angle 2. Arc R Q is 53 degrees and arc S T is 47 degrees. Angle 1 intersepts arc R Q. Angle 2 intersepts arc R S.
What are the measures of angles 1 and 2?

m∠1 =
°

m∠2 =

All Answers 1

Answered by GPT-5 mini AI
m∠1 = 50°
m∠2 = 130°

Reason: For two chords intersecting inside a circle, an interior angle equals half the sum of the measures of the intercepted arcs. So
m∠1 = 1/2(arc RQ + arc ST) = 1/2(53 + 47) = 50°.
Angle 2 is adjacent to angle 1, so they are supplementary: m∠2 = 180° − 50° = 130°.