Question

How to prove that sum of exterior angles of a polygon equals 360 degree?

Answer 1

GIVEN: A polygon with ‘n’ number of sides , <1,<2,<3,<4,<5,…… <n are exterior angles & A,B,C,D,E…..are interior angles.

TO PROVE: <1 + <2 + <3 + <4 + <5 + ……<n = 360°

The sum of interior angles of any polygon

=(n-2)*180 ………(formula used)

PROOF: <1 + <A =180° ………(1)

<2 + <B = 180° ……………(2)

<3 + <C = 180° ………..(3)

<4 + < D = 180° ………..(4)

<5 + <E = 180° ……….(5)

And so on up to n times..

By adding all above (1)+(2)+(3)+(4)+(5)+….(n)

<1+<2+<3+<4+<5+…….<n = 180°n - (A+B+C+D+E+…..n)

= 180n -{ ( n-2)*180 }

= 180n - 180n + 2*180

= 2*180

= 360°

=> <1+<2+<3+<4+<5+…..<n = 360°

[ HENCE PROVED] ●

Answer 2

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