In triangle PQR, PQ = PR and angle QPR = 48°. The side QR is extended beyond R to a point S. Find angle PRS.
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Worked Solution
Step 1: Use the isosceles triangle property.
Since PQ = PR, the base angles are equal.
Angle PQR = Angle PRQ
Step 2: Apply the angle sum of a triangle.
Angle PQR + Angle PRQ + Angle QPR = 180°
2 × Angle PRQ + 48° = 180°
2 × Angle PRQ = 132°
Angle PRQ = 66°
Step 3: Use the angles-on-a-straight-line property.
QR extended to S means PRQ and PRS are supplementary.
Angle PRS = 180° − 66° = 114°
Answer: Angle PRS = 114°
Answer: 114°
Correct answer: 114°
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