1. 12-3: Angles of Polygons Big Ideas Math, Course 2
What is the sum of the interior angles of a 102-sided shape?

2. One triangle = 180⁰ Two triangles = 180 + 180 360⁰ Four triangles =
Conceptualizing Triangles Within Polygons
What is the total angle measure?
One triangle =
180⁰
Two triangles =
360⁰
Four triangles =
4 • 180
720⁰

3. Knowing the Academic Language
Interior Angle Measures of a Polygon
The sum S of the interior angle measures of a polygon with n sides is:
S = (n – 2) • 180⁰
Shape
Sides
Formula
Sum
Triangle 3
(3 – 2) • 180
180⁰
Rectangle 4
(4 – 2) • 180
360⁰
Pentagon 5
(5 – 2) • 180
540⁰
Octagon 8
(8 – 2) • 180
1080⁰
Decagon 10
(10 – 2) • 180
1440⁰

4. Example 1
Find the sum of the interior angle measures of the shape.
a. A 102 sided figure (or a 102-gon)
S = (102 – 2) • 180⁰
S = 100 • 180
S = 18000⁰

5. Finding an Interior Angle Measure of a Polygon
To find an interior angle measure:
Step 1: Find the sum of the interior angle measure.
Step 2: Write and solve an equation to find missing angle measure.
Find the value of x.
140⁰ x⁰
128⁰
130⁰
120⁰
115⁰
145⁰
Step 1: S = (7 – 2) • 180⁰
S = 900⁰
Step 2:
x = 900
778 + x = 900
x = 122

6. Example 2 Find the value of x. Step 1: S = (5 – 2) • 180⁰ S = 540⁰
145⁰
2x⁰
110⁰
Step 1: S = (5 – 2) • 180⁰
S = 540⁰
Step 2:
x x = 540
400
+ 4x
= 540
4x = 140
x = 35

7. Regular Polygons and Their Angle Measures
Regular polygon – all the sides are congruent and all the interior angles are congruent
For example: What is the angle measures of a regular octagon?
Step 1: Find the sum of the interior angle measures.
S = (8 – 2) • 180⁰
S = 1080⁰
Step 2: Divide the sum by the number of interior angles.
1080 ÷ 8 =
135⁰

8. Finding Exterior Angle Measures
Exterior Angle Measures of a Polygon
The sum of the measures of the exterior angles of a polygon is 360⁰. e⁰ a⁰ d⁰ b⁰
a + b + c + d + e = 360 c⁰

9. Examples

10. Turn to Page 286 in your RAPJ
Practice
Turn to Page 286 in your RAPJ
and do 3, 5, 6 problems