Question

Three angles of an irregular octagon are 100 degrees, 120 degrees, and 140 degrees. The remaining angles are congruent. Find the size of each of the remaining angles

Answer 1

144°

Explanation:

The sum of the interior angles of a polygon is

sum = 180° × (n - 2) ← n is the number of sides

Here n = 8 ( octagon ), hence

sum = 180° × 6 = 1080°

let the measure of 1 congruent angle be x

Then sum the 8 angles and equate to 1080

100 + 120 + 140 + 5x = 1080

360 + 5x = 1080 ( subtract 360 from both sides )

5x = 720 ( divide both sides by 5 )

x = 144

Thus each of the 5 congruent angles is 144°