What are the size of each exterior angle in a regular polygon...?

Question

hello,
can somebody please help me with this question? :) ...
it says:

Find the size of each exterior angle in a regular polygon which has
a) 8 sides
b) 18 sides
c) 12 sides

Could sombody please tell me the formula and how to do it ?.. i would be very grateful

Thankyou.

Answer 1

Process will be the same for all three questions

a)



int. angle=360/8

int. angle=45 deg

exterior angle=180-45

=135deg.

Answer 2

I might be wrong, but I thought exterior angle was simply 360°-interior angle ( I am thinking in reference to the previous answer, which my understanding contradicts).



The sum of the interior angles of a polygon is (n-2)*180 where n= number of sides. In a regular polygon, the angles are all equal, so all you need to do is divide the sum by the number of angles to get a single interior angle and subtract that from 360 to get the exterior angle.



But let's play with the equations for a sec to find a simpler rule:



X=360-((n-2)*180/n) = 360-(n*180/n-360/n) = 360-180 +360/n = 180+360/n

which is pretty close to what that other answer said. Maybe I misread it.



Perhaps exterior angle is the angle that combines with the interior angle to make a line? Then that other answer is correct.

Answer 3

The exterior angles always total 360deg, so you just have to divide 360 by 8, 18, or 12 to get your three answers.