Question

the exterior angle of a regular polygon is one third of its interior angle find the number of sides in the polygon​

Answer 1

For a moment I thought this would be fairly easy. But only for a moment.

Then I thought logically. It hurts, but sometimes it’s worth the suffering.

Let’s start with a triangle. Interior angle 60 degrees, exterior angle 300 degrees. The exterior angle is not 1/3 od the interior angle. It’s much, much bigger.

Trying a square we get 90 and 270. Once again, the interior is much less than the exterior angle.

Going all the way to a circle, treating it as a polygon with an infinite number of sides, the interior angle is 180 and the exterior angle is 180. We still do not get an exterior angle one thirf the interior angle,and never will.

Reversing the question.. interior angle one third the exterior angle, we end up with a square. I ;eave it as an exercise for the reader to work out how many sides that has.

Answer 2

ANSWER==

71/3rd of the interior angle of the polygon.

The interior angle plus the exterior angle make a straight line, which is 180 degrees.

3x + (x - 20) = 180

4x = 200

x = 50

Interior angle = 150 degrees.

Let n = number of sides of this polygon.

180(n - 2) = sum of interior angles

180(n - 2) = 150n

30n = 360

n = 12

hope it helps!!