Question

Qs 4. By finding the size of each exterior angle of a regular polygon with 24 sides, calculate the size of each interior angle of the polygon.​

Answer 1

The sum of the exterior angles is 360 degrees. Each of the exterior angles = 360/24 = 15 degrees.

Answer 2

Step-by-step explanation:

We know that sum of exterior angle of polygon is 360°.

Now,

(Sum of exterior angle)/(number of sides) = size of each exterior angle

Assume that size of each exterior angle is x.

Substitute the values,

→ 360°/24 = x

→ 15° = x

So, the each of the exterior angle is of 15°.

Now,

Exterior angle = 180° - Interior angle

Substitute the values,

→ 15° = 180° - Interior angle

→ Interior angle = 180° - 15°

→ Interior angle = 165°

Hence, the the size of each interior angle of the ppolygo is 165°.

Additional Information:

Sum of polygon interior angles = (n - 2) × 180°

Polygon interior angles = [(n - 2) × 180°]/n

Exterior angle = 180° - Interior angle

Sum of angles = n × Exterior angle