What is the measure, in degrees, of each interior angle of a regular octagon (an 8-sided r… — JAMB UTME

What is the measure, in degrees, of each interior angle of a regular octagon (an 8-sided regular polygon)?

Answer: 135 degrees

Each interior angle of a regular octagon measures 135 degrees.

The sum of the interior angles of a polygon with

n

sides is

(n - 2) \times 180^\circ

. For a regular octagon (

n = 8

), the total interior angle sum is

(8 - 2) \times 180^\circ = 1080^\circ

. Since all 8 interior angles of a regular octagon are congruent, dividing the total sum by 8 yields

135^\circ

for each interior angle.

Find the sum of all interior angles of the regular octagon.

Sum of interior angles =

(8 - 2) \times 180^\circ = 6 \times 180^\circ = 1080^\circ

The sum of interior angles for any

n

-sided polygon is

(n - 2) \times 180^\circ

Calculate the measure of a single interior angle.

Interior angle =

\frac{1080^\circ}{8} = 135^\circ

In a regular polygon, all interior angles are equal in measure.

Interior Angle of a Regular Polygon

Question