if pqrst is a regular pentagon and STM is an isosceles triangle with sides TS is equal to TM then find the measure of the angle PTM
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Answer:
∠PTM = 144°
Step-by-step explanation:
Sum of interior angles of a pentagon = 540°
∠P = ∠Q = ∠R = ∠S = ∠T = 108°
∠PST + ∠TSM = 180°
=> 108° + ∠TSM = 180°
=> ∠TSM = 72°
∠TSM = ∠TMS (as TS = TM)
∠TSM + ∠TMS + ∠STM = 180°
=> 72° + 72° + ∠STM = 180°
=> ∠STM = 36°
∠PTM = ∠PTS + ∠STM
=> ∠PTM = 108° + 36°
=> ∠PTM = 144°
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