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In triangle ABC, AB = AC and angle A = 36°. The bisector of angle B meets AC at D. What is the measure of angle BDC?

Competition practiceGeometry
  • A72°
  • B108°
  • C60°
  • D36°

Step-by-Step Solution

The triangle is isosceles, so angle B = angle C = (180° − 36°)/2 = 72°. The bisector gives angle DBC = 36°. In triangle BDC, angle BDC = 180° − 36° − 72° = 72°.
Answer: A) 72°

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