Geometry and TrigonometryMediumVertex angle of an isosceles triangle
Geometry and Trigonometry practice question
In triangle PQR, PQ = PR and the measure of angle Q is 65°. What is the measure of angle P?
- A. 50°Correct
- B. 65°
- C. 115°
- D. 25°
Answer: A. 50°
Since PQ = PR, the angles opposite those sides — angles R and Q — are equal, so angle R is also 65°. Then angle P = 180 − 65 − 65 = 50°.
Why the other answers are wrong
- B. 65°
- 65° is the measure of angle Q (and R), the base angles. Angle P is the vertex angle, which is different.
- C. 115°
- 115° is 180 − 65, subtracting only ONE base angle. Both base angles are 65°.
- D. 25°
- 25° halves the vertex angle. The full vertex angle is 180 − 130 = 50°.
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