In triangle ABC, AB = AC and angle BAC = 36°. Point D lies on AC such that BD = BC. Find angle ABD.
Need a hint?
Find angle ABC first, then work out angle CBD in triangle BCD before subtracting.
Worked answer
- Angle ABC = angle ACB = (180° − 36°) ÷ 2 = 72°, since AB = AC.
- Triangle BCD is isosceles with BD = BC, so angle BDC = angle BCD = 72°.
- Angle CBD = 180° − 72° − 72° = 36°.
- Angle ABD = angle ABC − angle CBD = 72° − 36° = 36°.
Answer: 36 °
The mistake this question tests
Habit
Angle facts (straight line, triangle, quadrilateral)
Pupils stop at angle ABC = 72° and forget to subtract angle CBD, or they subtract the wrong angle from 72°.
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