1. Concept: Angle Measures in Polygons
Date:
Sec 8-1
Concept: Angle Measures in Polygons
Objective: Given a polygon, determine the measures of angles as measured by a s.g.

2. Sum of the measures of the interior angles in a polygon
Sum of interior angles = (n-2)180,
Where n = number of sides

3. Example 1: Find the value of x
= 456
=84
S= (n-2)180
S=(5-2)180
S=540

4. Example 2: Find the value of x
S= (n-2)180
S=(8-2)180
S=(6)180
S=1080
X= 1080/8
X = 135 X

5. Example 3: The sum of the measures of the interior angles in a convex polygon is given. Classify the polygon by the number of sides.
B. 360 A

6. Example 4: Find the measure of each angle in a regular 11-gon
(11-2)180 11
Each angle = 147.3

7. Example 5: The measure of each interior angle of a regular polygon is How many sides does the polygon have?
(n-2)180 = 165 n
Cross mult.
(n-2)180 = 165n
180n-360 = 165n
-180n n
-360 = -15n
24 = n

8. Sum of the exterior angles in a polygon is always 360
Example 6: What is the measure of each exterior angle in a regular hexagon?
=360/6
=60

9. Example 7: Find the value of x

10. Example 8: The measure of each exterior angle of a regular polygon is 40. How many sides does the polygon have?
360/40
=9 sides

11. Example 9:

12. Wrap-up: How do you find the sum of the interior angles in a polygon?
How do you find the sum of the exterior angles in a polygon?
Why do you need to know this?

13. Today’s Work