What is the size of each interior angle of a polygon that has 8 sides?

Answer 1

Any value greater than 0° and less than 360° except 180°, as long as the sum of all the 8 angles is 1080°.

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If you meant a REGULAR polygon that has 8 sides, then:

There are two ways to solve this:

• Use exterior angles:

The sum of the exterior angles of a polygon is 360°.

For a regular polygon each exterior angle is 360° ÷ number_of_sides

→ for an 8 sided polygon (an octagon), this is:

exterior_angle = 360° ÷ 8 = 45°

Now for any polygon:

exterior_angle + interior_angle = 180°

→ interior_angle = 180° - exterior_angle

→ for the regular octagon, interior_angle = 180° - 45° = 135°

• Use interior angles:

The sum of the interior angles of a polygon is given by:

sum_interior_angles = (number_of_sides - 2) × 180°

For an octagon, this gives:

sum_interior_angles = (8 - 2) × 180° = 6 × 180° = 1080°

In a regular polygon all the angles are the same, thus

sum_interior_angles = number_of_sides × interior_angle

→ interior_angle = sum_interior_angles ÷ number_of_sides

→ for the regular octagon, interior_angle = 1080° ÷ 8 = 135°