Question

The angles of a pentagon are a, (a+10), (a+20), (a+30), (a+40). Work out the size of the largest angle of the pentagon.

Answer 1

128°

Explanation:

Pentagon: has 5 sides

Let n be the number of sides of the polygon (pentagon).

a + (a+10) + (a+20) + (a+30) + (a+40) = (n-2) × 180

a + a + 10 + a + 20 + a + 30 + a + 40 = 3 × 180

5a + 100 = 540

5a = 540 - 100

= 440

a = 440 ÷ 5

= 88

Largest angle of the pentagon = (a+40)°

= 88° + 40°

= 128°

Answer 2

largest angle = 128°

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 , then

sum = 180° × 3 = 540°

Sum the interior angles and equate to 540

a + a + 10 + a + 20 + a + 30 + a + 40 = 540 , that is

5a + 100 = 540 ( subtract 100 from both sides )

5a = 440 ( divide both sides by 5 )

a = 88

Then

largest angle = a + 40 = 88 + 40 = 128°