Geometry and TrigonometryVery hardAngle in a triangle with a second isosceles triangle inside
Geometry and Trigonometry practice question
In triangle ABC, AB = AC and angle A measures 36°. Point D lies on AC so that BD = BC. What is the measure, in degrees, of angle DBC?
Answer: 36
The base angles of ABC are 72° each. In triangle BDC, BD = BC, so angle BDC = angle BCD = 72°, leaving angle DBC = 180 − 144 = 36.
Common wrong answers
- If you answered 54
- 54 halves 108.
- If you answered 72
- 72 is a base angle, not angle DBC.
- If you answered 108
- 108 is angle ADB.
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