Math, asked by ompandya816, 10 months ago

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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Answers

Answered by amitnrw
9

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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