Geometry and TrigonometryVery hardAngle in a triangle with an altitude
Geometry and Trigonometry practice question
In triangle PQR, angle P measures 40° and angle Q measures 90°. An altitude is drawn from Q to side PR, meeting it at point S. What is the measure, in degrees, of angle SQR?
Answer: 40
Angle R = 180 − 40 − 90 = 50°. In right triangle QSR (right angle at S), angle SQR = 90 − 50 = 40°. (Equivalently, the altitude from the right angle creates triangles similar to the original.)
Common wrong answers
- If you answered 45
- 45 assumes the altitude bisects the right angle, which it does only in an isosceles right triangle.
- If you answered 50
- 50 is angle R (and angle PQS), not angle SQR.
- If you answered 90
- 90 is angle Q as a whole; the altitude splits it into 50° and 40°.
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