A triangular road sign near Toa Payoh MRT is shaped like triangle PQR, where PQ = PR. The exterior angle of the triangle at Q (formed by extending side PQ beyond Q) measures 118°. A line QS is drawn from Q to a point S on PR such that QS bisects the exterior angle at Q. Find angle QSR.
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Worked Solution
Step 1: Find the interior angle at Q:
Interior angle PQR = 180° − 118° = 62°
Step 2: Since PQ = PR, triangle PQR is isosceles, so the base angles are equal:
angle PRQ = angle PQR = 62°
Apex angle QPR = 180° − 62° − 62° = 56°
Step 3: QS bisects the exterior angle at Q:
angle RQS = 118° ÷ 2 = 59°
Step 4: Apply angle sum in triangle QSR:
angle QSR = 180° − angle QRS − angle RQS
angle QSR = 180° − 62° − 59° = 59°
Correct answer: 59°
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