Date:

Sec 8-1Concept: Angle Measures in Polygons

Objective: Given a polygon, determine the measures of angles as

measured by a s.g.

Sum of the measures of the interior angles in a polygon

Sum of interior angles = (n-2)180,

Where n = number of sides

Example 1: Find the value of x

j

A

C

D

E

105

X

114

135

102

S= (n-2)180

S=(5-2)180

S=540

114+105+102+135 = 456

540-456 =84

Example 2: Find the value of x

X

S= (n-2)180

S=(8-2)180

S=(6)180

S=1080

X= 1080/8

X = 135

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.

A. 1980 B. 360

Example 4: Find the measure of each angle in a regular 11-gon

(n-2)180

n

(11-2)180

11

Each angle = 147.3

Example 5: The measure of each interior angle of a regular polygon is 165. How many sides does the polygon have?

(n-2)180 = 165

n

Cross m

ult.(n-2)180 = 165n

180n-360 = 165n

-180n -180n

-360 = -15n

-15 -15

24 = n

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

Example 7: Find the value of x

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

Example 9:

Wrap-up:

1. How do you find the sum of the interior angles in a polygon?

2. How do you find the sum of the exterior angles in a polygon?

3. Why do you need to know this?

Today’s Work