Question

The interior angles of a pentagon are x, (x+20), (x + 20), (x + 40) and (x + 40). Work out the value of x.​

Answer 1

x = 84

Explanation:

the sum of the interior angles of a polygon is

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

a pentagon has 5 sides , so n = 5

sum = 180° × (5 - 2) = 180° × 3 = 540°

sum the interior angles and equate to 540

x + x + 20 + x + 20 + x + 40 + x + 40 = 540

5x + 120 = 540 ( subtract 120 from both sides )

5x = 420 ( divide both sides by 5 )

x = 84