AlgebraMediumVertex angle of an isosceles triangle
Algebra practice question
In an isosceles triangle, the vertex angle is 30° less than each of the two equal base angles. What is the measure, in degrees, of the vertex angle?
Answer: 40
Let each base angle be b: 2b + (b − 30) = 180 → 3b = 210 → b = 70. The vertex angle is 70 − 30 = 40.
Common wrong answers
- If you answered 30
- 30 is the difference, not the angle.
- If you answered 50
- 50 comes from 3b + 30 = 180, adding the 30 instead of subtracting.
- If you answered 70
- 70 is each base angle.
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