1. Chapter 8
Polygons and Area

2. Section 2 Angles in Polygons

3. The definitions for interior angles and exterior angles can be extended to include angles formed in any polygon. In the diagrams shown below, interior angles are red, and exterior angles are blue.

4. Shape
Sides (n)
n-2
180 * (n-2)
Sum of Degrees of interior angles
triangle
quadrilateral
pentagon
nonagon

5. Example 1: Use the Polygon Interior Angles Theorem Find the sum of the measures of the interior angles of a convex heptagon.

6. Example 2: Find the Measure of an Interior Angle Find the measure of <A in the diagram.

7. Example 3: Interior Angles of a Regular Polygon Find the measure of an interior angle of a regular octagon.

8. Checkpoint: Find Measures of Interior Angles In 1-3, find the measure of <G.

9. Checkpoint: Find Measures of Interior Angles 4) Find the measure of an interior angle of a regular polygon with twelve sides.

11. Sum of Degrees of exterior angles
Type equation here.
Shape
Sides (n)
angles
Sum of exterior angles
Sum of Degrees of exterior angles
triangle
m∠1+m∠2+m∠3=360
quadrilateral
m∠1+m∠2m+m∠3+m∠4=360
pentagon
nonagon

12. Example 4: Find the Measure of an Exterior Angle Find the value of x.
m∠1 + m∠2+m∠3+ x = 360
m∠1 = m∠3 = 2x
m∠2= m∠4 = x
x + x=360
180+2x=360
x+x=360
180+3x=360
2x =
3x=180
X= 180
X = 60

13. 269 + =360 x=91 73+60+90+x+46=360 116+92+89+3X =360 297+3X=360 3X = 63
Checkpoint: Find Exterior Angle Measures Find the value of x.
X =360
297+3X=360
3X = 63
X = 21
x+46=360
269 +
=360 X •
x=91

14. Checkpoint: Find Exterior Angle Measures Find the value of x.

15. EXIT SLIP