Mathematics
In the given figure, find the value of a + b + c + d + e + f.
Triangles
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Answer
In △AED,
⇒ a + b + ∠A = 180° ….(1)
In △DBF,
⇒ c + d + ∠B = 180° ….(2)
In △EFC,
⇒ e + f + ∠C = 180° ….(3)
In △ABC,
⇒ ∠A + ∠B + ∠C = 180° ….(4)
Adding eq.(1), (2) and (3), we get :
⇒ a + b + c + d + e + f + ∠A + ∠B + ∠C = 180° + 180° + 180°
⇒ a + b + c + d + e + f + 180° = 540°
⇒ a + b + c + d + e + f = 540° - 180°
⇒ a + b + c + d + e + f = 360°.
Hence, the value of a + b + c + d + e + f = 360°.
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