Triangle PQR has PQ = PR and angle QPR = 80°. Point S lies on QR such that QS = QP.
- Find angle QPS.
- Find angle PSR.
Need a hint?
Look for two equal sides first. In triangle PQS, which two angles are equal, and what does the straight line QR tell you about angle PSR?
Worked answer
- Triangle PQR is isosceles with PQ = PR, so angle PQR = (180° − 80°) ÷ 2 = 50°.
- In triangle PQS, QS = QP, so it is isosceles with equal base angles at P and S.
- Angle PQS = 50°, so angle QPS = (180° − 50°) ÷ 2 = 65°.
- Angle QSP = 65° as well, so angle PSR = 180° − 65° = 115°.
Answer: 115 °
The mistake this question tests
Habit
Angle facts (straight line, triangle, quadrilateral)
Pupils subtract the base angle at Q from 180° to get 130°, forgetting that the angle at S is equal to angle QPS, not angle PQS.
How to fix it at home →More PSLE geometry & angles questions
Structured · 3m
Triangle ABC is equilateral
See the answer →Short answer · 2mA parallelogram ABCD has angle ABC = 118° and angle BAC = 37°
See the answer →MCQ · 1mKLMN is a trapezium with KN parallel to LM
See the answer →Short answer · 2mIn triangle ABC, AB = AC and angle BAC = 36°
See the answer →Short answer · 2mA robot vacuum turned 270° clockwise and then stopped
See the answer →Structured · 4mA rectangle is made by placing 4 identical squares side by side in a row
See the answer →Practise PSLE geometry & angles until the mistakes stop.
Three PSLE questions, free, no sign-up. You’ll see exactly where the marks went. Then 7 days of everything for S$4.99.