Question

Measures of one exterior angle of a regular polygon is greater than one of interior angle

Answer 1

Define x:

Let the number of sides be x

Find one exterior angle:

Sum of exterior angle = 360

One exterior angle = 360 ÷ x = 360/x

Find one interior angle:

Sum of interior angles = (n - 2) x 180

Sum of interior angles = (x - 2) x 180

Sum of interior angles = 180x - 360

One interior angle = (180x - 360)/x

Given that the exterior angle is greater than the interior angle:

360/x > (180x - 360)/x

360/x > (180x - 360)/x

360 > 180x - 360

180x - 360 < 360

180x < 720

x < 4

⇒ x = 3

A polygon with 3 sides = triangle

Answer: The polygon is a triangle