Geometry and TrigonometryVery hardAngle split by the altitude of an isosceles triangle
Geometry and Trigonometry practice question
In triangle PQR, PQ = PR and the measure of angle P is 40°. Point S lies on QR so that PS is perpendicular to QR. What is the measure, in degrees, of angle QPS?
Answer: 20
In an isosceles triangle the altitude from the apex bisects the apex angle: angle QPS = 40 ÷ 2 = 20.
Common wrong answers
- If you answered 40
- 40 is the whole apex angle.
- If you answered 50
- 50 is 90 − 40.
- If you answered 70
- 70 is a base angle (angle Q or R).
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