Question

An n-sided polygon has interior angles of which 4 of them are of sizes 125,220,40 and 295 degrees . The remaining interior angles are of sizes 20 degrees each. Find the value of n,


My working:
let the number of sides for the polygon be n and the remaining number of sides be x.
(n-2)x 180 = 125+220+40+295+20x
180n-360=680+20x
180n=680+20x+360
180n=1040+20x

Answer 1

Good idea, but you don't need x. There are n sides and n angles. Since you already have 4 angles, there are n-4 remaining. So,

(n-2)180 = 125+220+40+295+20(n-4)
n=6

Answer 2

Why is the answer n=6 ?

Answer 3

It's alright. Thank you for your help.