## kamuela710 Group Title If the measure of an exterior angle of a regular polygon is 24, how many sides does the polygon have? 2 years ago 2 years ago

1. GT Group Title

exterior angle? Can you draw which one it is?

2. moneybird Group Title

360/n = 24

3. moneybird Group Title

n is the number of sides

4. MrYantho Group Title

To do this, we have to remember two things: 1. The exterior angles of a polygon ALWAYS add up to 360 degress 2. A regular polygon's angles are all equal (including exterior) So, every exterior angle is 24 $n=360/24$ $n=15$

5. GT Group Title

How is it then called exterior angle? That is the angle between two adjacent vertices and the center of the polygon.

6. moneybird Group Title

i think exterior angle is 180 - interior angle

7. moneybird Group Title

|dw:1327116266165:dw|

8. GT Group Title

How can that be 24 for a polygon?

9. MrYantho Group Title

|dw:1327116301791:dw| Interior and exterior angles sum to 180

10. moneybird Group Title

It's 24 sides

11. GT Group Title

See that drawing helped.

12. GT Group Title

OK. Then, the interior angle is 156. So, the angle at the center of the polygon must be 24 also. Therefore, 360/24 sides. Got it.

13. MrYantho Group Title

Nope. There are 15 sides (see earlier answer). Exterior angles always sum to 360 no matter how many sides. So it is n=360/24 The sum of interior angles is different depending on the number of sides: $\sum=(n-2)*180$ where n is the number of sides.

14. GT Group Title

360/24 = 15. What is the issue there?

15. MrYantho Group Title

Sorry, that was a misread by me. :-P

16. GT Group Title

BTW - I hate that "formula" thing with n-2 thing. It is unnecessary. Basic triangle property of angles and the circle being 360 degrees does the trick here, and then it is all basic arithmetic.

17. MrYantho Group Title

I completely agree. It's just a much longer explanation for a forum like this.

18. GT Group Title

Yeah. But, I like calculating knowing geometric properties rather than having people memorize a formula.