Question

How many sides does a regular polygon have if one exterior angle is 1 degree

Answer 1

Step-by-step explanation:

As we are dealing with a regular polygon, if one exterior angle is 1°, then all of the exterior angles are 1°.

Imagine you are standing at one vertex (vertex 1) of this polygon and start walking clockwise along the perimeter. At the next vertex, vertex 2, you turn 1°. and carry on walking. At the next vertex, vertex 3, you again turn 1° and carry on walking. And so on. By the time you return to vertex 1, you have turned through a total angle of 360°. A you are turning 1° at each vertex, to turn through 360° means that you turn 360 times. Thus, there are 360 vertices and hence 360 sides to the polygon.