Question

The diagram shows a star made by surrounding a

regular octagon with triangles.
Explain why angle a must be 135°.
a

Answer 1

Explanation:

the formula to calculate the sum of interior angles of a polygon is given by (n - 2) × 180°.

So, since the octagon has 8 sides, the sum of the interior angles will be (8 - 2) × 180° = 1080°.

1080 : 8 = 135°

Answer 2

see explanation

Explanation:

the sum of the interior angles of a polygon is

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

an octagon has 8 sides , then

sum = 180° × 6 = 1080°

the octagon has 8 congruent interior angles , then

a = 1080° ÷ 8 = 135°