The size of each interior angle of a regular polygon is 168°. Find tge number of sides of the polygon

Answer 1

Let n be the number of sides of the regular polygon. Each interior angle of an n-sided polygon is given by the formula:

Interior angle = (n-2) × 180° / n

We are given that the size of each interior angle is 168°, so we can set up an equation:

168 = (n-2) × 180 / n

Multiplying both sides by n, we get:

168n = 180(n-2)

Expanding the right side, we get:

168n = 180n - 360

Subtracting 168n from both sides, we get:

12n = 360

Dividing both sides by 12, we get:

n = 30

Therefore, the regular polygon has 30 sides.

Answer 2

Calculate the size of one exterior angle of an 18 sided regular polygon

Answer 3

The sum of the exterior angles of a polygon is always 360°. For a regular polygon with n sides, each exterior angle has a size of:

Exterior angle = 360° / n

For an 18-sided regular polygon:

Exterior angle = 360° / 18 = 20°

Therefore, each exterior angle of an 18-sided regular polygon has a size of 20°.