## 28Tylerr 3 years ago Find the sum of the measures of the interior angles of each convex polygon.

1. luck4u

overall

2. 28Tylerr

Here is the question: 16-gon

3. luck4u

???

4. luck4u

i dont know

5. 28Tylerr

It wants me to find the sum of a convex polygon and the polygon is a 16-gon

6. 28Tylerr

& I can't seem to figure it out.

7. .Sam.

Use the formula (n-2)*180

8. 28Tylerr

Ok, So would it be 16 in place of the n?

9. .Sam.

You will get 2520 degrees

10. 28Tylerr

Ok, But what number would I put in place of the n?

11. .Sam.

16

12. 28Tylerr

Alright thanks man, Can ya help me with a couple of more?

13. .Sam.

ok

14. 28Tylerr

My next one is: The measure of the interior angles of a regular polygon is given. Find the number of sides in the polygon.

15. 28Tylerr

Here is the question: 1980.

16. .Sam.

Sum of the angles is 1980?

17. 28Tylerr

I just got to find the polygon that has a number of sides of 1980.

18. 28Tylerr

Thats basically what it is.

19. 28Tylerr

..Sam, Can ya help?

20. .Sam.

$\frac{(n-2)\times180}{n}=\text{Each \angle inside the polygon}$ $(n-2)\times180=\text{Sum of angles inside the polygon}$ ---------------------------------------------------------- So, $(n-2)\times180=\text{Sum of angles inside the polygon}$ $(n-2)\times180=1980$ n=13

21. 28Tylerr

Alright thanks, Can ya help with 4 more lol? Sorry man

22. .Sam.

post as a new question

23. 28Tylerr

Alright, Give me a min

24. SmoothMath

The equation is (180)(n-2), where n is the number of sides. Here's why: |dw:1334620067825:dw| The number of triangles that I can split the polygon up into, is n-2. Each triangle's interior angles sum to 180. How cool! =D