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Question
In the given figure, ∠RST = 56°, seg PT ⊥ ray ST, seg PR ⊥ ray SR and seg PR ≅ seg PT. Find the measure of ∠RSP. State the reason for your answer.
Solution
seg PT ⊥ ray ST, seg PR ⊥ ray SR ...[Given]
seg PR ≅ seg PT
∴ Point P lies on the bisector of ∠TSR ...[Any point equidistant from the sides of an angle is on the bisector of the angle]
∴ Ray SP is the bisector of ∠RST.
∠RSP = 56° ...[Given]
∴ ∠RSP = `1/2 `∠RST
= `1/2 xx56°`
∴ ∠RSP = 28°
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