In the given figure, prove that P+2Q+ ZR + 2S + 2T = 2 x right angles T
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Answer:
Correct option is A)
Sum of angles on a straight line=180
∘
⟹∠PAE=180
∘
−∠1
Similarly,∠PEA=180
∘
−∠5
In△PAE
∠PAE+∠PEA+∠APE=180
∘
⟹180−∠1+180−∠5+∠APE=180
∘
⟹∠APE=∠1+∠5−180
∘
=∠P
Similarly,∠BSC=∠2+∠3−180
∘
=∠S
∠DRC=∠3+∠4−180
∘
=∠R
∠DQE=∠4+∠∠5−180
∘
=∠Q
∠ATS=∠1+∠2−180
∘
=∠T
⟹∠P+∠Q+∠R+∠S+∠T
=∠1+∠2+∠3+∠4+∠2+∠3+∠4+∠5+∠1+∠5−(180×5)
=2(∠1+∠2+∠3+∠4+∠5)−900−(1)
From pentagon ABCDE,
Sum of angles of pentagon=((2×5)−4)×90
∘
(∵ Sum of angles=(2n−4)×90 )
=6×90=540
∘
⟹∠P+∠Q+∠R+∠S+∠T=2(540
∘
)−900
∘
=1080
∘
−900
∘
=180
∘
=2×90
=2Rightangles
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