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Question
ΔPQR is equilateral. PR = RS.
∴ find ∠RPS.
Options
60°
90°
30°
120°
MCQ
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Solution
30°
Explanation:
Since ΔPQR is equilateral, each angle is 60°.
Given PR = RS, triangle PRS is isosceles.
The straight line at R makes the exterior angle of the equilateral triangle, so ∠PRS = 180° – 60° = 120°.
In isosceles triangle PRS, the remaining two angles are equal:
∠RPS = ∠RSP
= `(180^circ - 120^circ)/2`
= 30°
Therefore, ∠RPS = 30°.
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