Question

Five of the interior angles in a hexagon are the same size. The remaining angle is 30° smaller than the rest. What is the size of the smallest interior angle in the hexagon? Give your answer in degrees (°).​

Answer 1

smallest angle = 95°

Explanation:

the sum of the interior angles in a polygon is

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

a hexagon has 6 sides, then n = 6

sum = 180° × (6 - 2) = 180° × 4 = 720°

let x represent each of the 5 equal angles, then smaller angle = x - 30

Then

5x + x - 30 = 720

6x - 30 = 720 ( add 30 to both sides )

6x = 750 ( divide both sides by 6 )

x = 125

thus smallest angle = x - 30 = 125 - 30 = 95°