Use the first principle of induction to prove that the sum o

Use the first principle of induction to prove that the sum of the interior angles of an n-sided simple closed polygon is (n - 2) 180 degree for all n greaterthanorequalto 3. Use the second principle of induction to prove that the sum of the interior angles of an n-sided simple closed polygon is (n - 2)180 degree for all n greaterthanorequalto 3.

Solution

a) solving basic step put n=3 in above equation

n=3;

(n-2)*180;

(3-2)*180;

so 180 for 3 side...(a)

we know this is for triangle

2 step

we assume this is true of k

for k side

(k-2)*180;.......(2)

now we have to prove for ( k+1) side

(k+1-2)*180;

(k-2)*180+180

(k-2)*180 is proved by (2)

180 is proved by (1)

hence proved