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In the adjoining 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.

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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) x 56° 

∴ ∠RSP = 28°

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