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CDS 2025 · PYQ · Triangles / Angle Bisectors · medium

The measure of an angle formed by the bisectors of the angles A and C of the triangle ABC is 130°. What is the measure of the angle B?

  1. A.65°
  2. B.75°
  3. C.80°
  4. D.85°✓ Correct

Explanation

The angle formed at the intersection of the bisectors of angles A and C in triangle ABC equals 90° + B/2 (when measured on the side containing B) or 180° − (A/2 + C/2). Using 180° − (A+C)/2 = 130°, so (A+C)/2 = 50°, giving A + C = 100°. Then B = 180° − 100° = 80°. Hmm, but checking standard formula: the angle between bisectors of A and C, measured at their intersection, equals 90° + B/2. So 90° + B/2 = 130°, giving B/2 = 40°, hence B = 80°. The answer should be 80°, option (c). However if the question refers to a different angle (exterior), then 180 − 130 = 50 = 90 − B/2 ... actually let me reconsider. With angle = 90 + B/2 = 130°, B = 80°.
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