Question

please explain to me how to do theses questions.
Thanks.

Find the sum of the measures of the interior angles of a convex 18-gon.

How many sides does a regular polygon have if one interior angle measures 150?

What is the sum of the measures of the exterior angles of a convex 15-gon?

Answer 1

You can always divide these regular polygons into triangles. The number of triangles is 2 less than the number of sides. Since the angles of each triangle total 180 we can calculate the total of all the angles. Then we can divide that total by the number of angles (which is equal to the number of sides) and we have the measure of each angle.

Answer 2

Now let's try it on your first question about the 18-gon. That would make 16 triangles. 16(180)=2880. So the total of all 18 angles is 2880. Let's divide that by 18 to find the measure of each angle. 2880/18=160. That is the measure of each interior angle.

Answer 3

Now you try the second one.

Answer 4

k one sec

Answer 5

im suppose to work backwards right?

Answer 6

yes

Answer 7

...i dont know how to... :(

Answer 8

\[150=\frac{(n-2)(180)}{n}\]
Solve for n. That will be the number of sides.

Answer 9

n = 12 :D