How do i do this problem?

Question

The measure of each exterior angle of a regular polygon is twice the measure of each interior angle. How many sides does the polygon have?
whats the answer, is there any way to get it without drawing it

Thank you!

Answer 1

The polygon has 3 sides (a triangle). One theorem in geometry states that the sum of the exterior angles of any convex polygon sum to 360 degrees. In this case, 360 divided by 3 exterior angles results in 120 degrees. Therefore, each interior angle is 60 degrees, hence each exterior angle is twice the measure of each interior angle.

Answer 2

The sum of the exterior angles of a polygon must be 360 degrees ( the size of an angle of revolution)

We also know that this is twice the sum of the interior angles

Let e be the no of degrees of the exterior angles
Let i be the no of degrees of the interior angles

e =360
e =2 X i
i = e/2
i =360/2
=180
So the sum of the interior angles is 180 degrees

If a polygon has n sides, the sum of its interior angles is 180×(n-2).
180 = 180 X (n-2) divide both sides by 180
1 = 1 X (n-2)
1 = n - 2 add 2 to both sides
3 = n
so the number of angles in this figure is 3
It is a triangle

Answer 3

It's a Regular Hexagon. They have the same angle measurements on all interior angles (120 degrees) and twice as the measurement on the exterior angles. (240 degrees)

Answer 4

you cannot have a regular polygon that the exterior angles are twice the interior. the interior angles would be 80 degrees. you cannot draw such polygon

Answer 5

6 sides, each interior angle is 60 degrees while each exterior angle is 120 degrees

Answer 6

let x be the exterior angle angles
let x be the exterior andgle the 2x is the interior angles



x + 2x = 180
3x = 180
x = 60

n = 360/60
n = 6 sides