Asked by luhha
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°
Explanation: For two chords intersecting inside a circle, an angle equals half the sum of the measures of its intercepted arcs.
Angle 1 intercepts arcs RQ and ST, so m∠1 = 1/2(53° + 47°) = 50°.
Angle 2 is the adjacent (supplementary) angle to angle 1, so m∠2 = 180° − 50° = 130°. (Equivalently, m∠2 = 1/2(the other two arcs) = 1/2(360° − 100°) = 130°.)
m∠2 = 130°
Explanation: For two chords intersecting inside a circle, an angle equals half the sum of the measures of its intercepted arcs.
Angle 1 intercepts arcs RQ and ST, so m∠1 = 1/2(53° + 47°) = 50°.
Angle 2 is the adjacent (supplementary) angle to angle 1, so m∠2 = 180° − 50° = 130°. (Equivalently, m∠2 = 1/2(the other two arcs) = 1/2(360° − 100°) = 130°.)
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.