Question

A regular polygon has an interior angle which less than ten times its exterior angle by 84°.Find the sum of all its interior angle?

Answer 1

If the number of sides is n, then we have

180(n-2)/n = 10(360/n)-84
n=15

So, the sum of its interior angles is 180(15-2) = 2340°

Answer 2

let the number of sides be n
each interior angle = 180(n-2)/n
each exterior angle = 360/n

180(n-2)/n < 10(360/n) by 84
180(n-2)/n = 10(360/n) - 84
times n, which is positive
180(n-2) = 3600 - 84n
180n - 360 = 3600 - 84n
264n = 3960
n = 15

sum of angles = 180(15-2)° = 2340°

check my arithmetic