The ratio of interior to exterior angle in a reg. polygon is 2:3, whats the measure of an exterior angle?

Question

Also what is the polygon called?

Answer 1

180/5 = 36

the sum of an interior angle and exterior angle is 180 degrees.

a ratio of 2:3 means there are 5 divisions.





interior angle 72 (36*2)

exterior angle 108 (36*3)



360/72 = 5

a 5 sided figure is a pentagon,



http://www.mathsisfun.com/geometry/exterior-angles.html

Answer 2

The interior angle and exterior angle are supplementary so they add up to 180 degrees

So, if the ratio is 2:3 then the angles can be shown as

2x+3x=180

5x=180

x=36

so the interior angle is 2(36)=72 and the exterior angle is 3(36)=108



Wait, something is wrong here... there are no regular polygons with all the interior angles each measuring 72 degrees.



regular triangle= 60 degrees each

regular quadrilateral(square)= 90 degrees each

regular pentagon= 108 degrees each



My guess is the the ratio is turned around and supposed to say either: "the ratio of interior to exterior angle in a reg. polygon is 3:2" or "the ratio of exterior to interior angle in a reg. polygon is 2:3".



In either case, the polygon would be a pentagon with exterior angles each measuring 72 degrees.

Answer 3

By extension of one of the sides of the polygon.

Then the sum if the Interior and Exterior angles is 180 degrees . angled point on a straight line.



Then 180 is ratiod in 2:3 :: Int:Ext

180 / (2 + 3) x 2 = 72 (Interior angle)

180 / (2 + 3) x 3 = 108 (Exterior Angle) .



The name of the polygon is found by calculating the number of sides(n).



Int.Angle = 360 / n

72 = 360 / n

n = 360/72

n = 5



So the polygon has five(5) sides

A five-sided polygon is named a 'PENTAGON'.