Question

the number of sides of a regular polygon where each exterior angle has measure of
45 degree is
(A)8, (B)10 , (C)4 , (D)6

Answer 1

Step-by-step explanation:

interior and exterior angles for different regular polygons.

In a regular polygon the sides are all the same length and the interior angles are all the same size.

The following diagram shows a regular hexagon:

Note that, for any point in a polygon, the interior angle and exterior angle are on a straight line and therefore add up to 180°.

This means that we can work out the interior angle from the exterior angle and vice versa:

Interior Angle = 180° – Exterior Angle

Exterior Angle = 180° – Interior Angle

If you follow around the perimeter of the polygon, turning at each exterior angle, you do a complete turn of 360°.

In every polygon, the exterior angles always add up to 360°

Since the interior angles of a regular polygon are all the same size, the exterior angles must also be equal

Answer 2

Answer:

number of sides = 360/45

= 8