Question

Calculate the exterior angle of a regualr polygon in which the interior angle is five times the exterior angle. Hence state the number of sides in the polygon. Please help =).

Answer 1

The exterior angle is always 360.
The interior angle can be stated as:
180 * (n-2) for a regular n sided pylogon.
notice the triangle n = 3 => 180 * (3-2) = 180
Now you'll have to solve for n:
(180 * (n-2) ) = 5 * 360

Answer 2

Can you please explain step by step =/

Answer 3

I think the exterior angle refers to the angle that is outside (opposite) the interior angle. Thus it should be 360-angle of interior angle.

angle_exterior = 360deg - angle_interior

Answer 4

Do you mean for the question, that an exterior angle is 5 times the interior angle?

Answer 5

the interior angle is 5 times the exterior angle

Answer 6

I'm think the exterior angle of a regular polygon is constant and 360 deg.
Well looking at:
180 * (n-2) = 5* 360
This means that:
The interior angle of a n sided polygon is 180 * (n-2)
The the exterior angle times 5 equals the interior: 5 * 360
if you solve for n you'll get
180(n-2) = 5*360
n-2 = 5*360 / 180 = 10
n = 10 + 2 = 12
The polygon has 12 sides :)

Answer 7

I'm not 100% certain now.
I'm comparing the sum of the exterior and interior. I'm not sure if the question asks for a single interior angle and a single exterior.

Answer 8

The question is asking for the exterior angle and the number of sides of the polygon

Answer 9

Exterior angle: 30 deg
Number of sides: 12

Answer 10

Thank you very much! =)