1. 8.1 Angles of Polygons What you’ll learn:
To find the sum of the interior angles of a polygon.
To find the sum of the measures of the exterior angles of a polygon.

2. Diagonals
You can draw diagonals in any polygon that has more than 3 sides. Drawing all diagonals from one vertex creates triangles. For each side that is added, another triangle is also added (180 too). 4 sides 5 sides 6 sides 7 sides 8 sides 9 sides 2 s 3 s 4 s 5 s 6 s 7 s 360 540 720 900 1080 1260

3. Theorem 8.1
Interior Angle Sum Theorem If a convex polygon has n sides and S is the sum of the measures of its interior angles, then S=180(n-2). If a polygon is regular, then divide the total number of degrees by the number of sides to find the measure of each angle. How many degrees are there in a 20-gon? S=180(20-2) S=180(18) S=3240

4. Theorem 8.2
Exterior Angle Sum Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360. 1+2+3+4+5+6=360 1 2 3 4 5 6

5. Find the sum of the measures of the interior angles of each convex polygon.

6. The measure of an interior angle of a regular polygon is given
The measure of an interior angle of a regular polygon is given. Find the number of sides in each polygon.
140
157½

7. Find x. 7x
4x+5
5x-5
6x+10
4x+10
S=540 26x+20=540 26x=520 x=20

8. Homework p even