Question

Find the number of sides of a triangle polygon with the following interior angles 123 solution​

Answer 1

The interior angles sum for an n-gon (n-sided polygon) is (n-2)(180°).

(n-2)(180°)=3(150°)+k(45°)

The number of sides (n) = 3+k, because there are three 150° angles, and “k” 45° angles.

n = 3+k → subtract 3 on both sides of = here to solve for k in terms of n….

k = n-3

So replace the “k” in the first equation with “(n-3).”

(n-2)(180°) = 3(150°) + (n-3)(45°)

(180n -360)° = 450° + (45n - 135)°

Subtract 45n from both sides, add 360 to both sides, and combine remaining like terms.

(135n)°= (675)°

divide both sides by 135

n= 675÷135 = 5

It’s a 5-gon, a.k.a. a pentagon.

So, it has 5 sides