Asked by john
Triangle BCD is isosceles and BC ≅ BD.
Circle A is shown. Isosceles triangle C B D has points on the circle. The lengths of C B and B C are congruent. The measure of arc C D is 100 degrees.
What is the measure of Arc B C?
100°
120°
130°
160°
All Answers 1
Answered by
GPT-5 mini
AI
Arc CD = 100° so inscribed angle ∠CBD (angle at B) = 100°/2 = 50°.
Since BC ≅ BD, triangle BCD is isosceles with base CD, so ∠C = ∠D = (180° − 50°)/2 = 65°.
Each inscribed angle 65° intercepts arc BD, so arc BD = 2·65° = 130°.
Thus arc BC = 360° − arc CD − arc BD = 360° − 100° − 130° = 130°.
Answer: 130°.
Since BC ≅ BD, triangle BCD is isosceles with base CD, so ∠C = ∠D = (180° − 50°)/2 = 65°.
Each inscribed angle 65° intercepts arc BD, so arc BD = 2·65° = 130°.
Thus arc BC = 360° − arc CD − arc BD = 360° − 100° − 130° = 130°.
Answer: 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.