# Sum of inner angles

Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.

Result

d =  0

#### Solution:

$n=3 ... s_{ 3 }=180^\circ \ \\ n=4 ... s_{ 4 }=s_{ 3 } + 180^\circ \ \\ n=5 ... s_{ 5 }=s_{ 4 } + 180^\circ \ \\ s=180n - 360=180(n-2) \ \\ d=0$

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