SWBAT: Calculate Interior and Exterior Angles of Polygons
Interior
and
Exterior
Angles
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons
Convex
Irregular
Concave
Irregular
Convex
Regular
Concave
Irregular
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons
S=180(n-2)
S= Sum of interior angles
n= # of sides
SWBAT: Find measures of interior and exterior angles of polygons.
Example 1: Calculating the Sum of Interior Angles
Find the sum of the interior angles of a decagon.
S= ?
n= 10
S=180(n-2)
S=180(10-2)
S=180(8)
S=1440°
SWBAT: Find measures of interior and exterior angles of polygons.
Example 2: Calculating the measure of each of interior Angle of any regular
polygon
What is the measure of each interior angle
of a regular octagon?
i = ?
n = 8
i =
i =
i =
𝟏𝟖𝟎(𝒏−𝟐)
𝒏
𝟏𝟖𝟎(𝟖−𝟐)
𝟖
𝟏𝟎𝟖𝟎
𝟖
i = 135
SWBAT: Find measures of interior and exterior angles of polygons.
Example 3: Calculating the number of sides of a polygon given the sum of the
interior angles
The sum of the interior angles of a convex regular polygon
measure 1980, how many sides does the polygon have?
S= 1980°
n= # of sides
S=180(n-2)
1980=180(n-2)
180 180
11 = n - 2
+2 =
+2
13 = n
SWBAT: Find measures of interior and exterior angles of polygons.
Exterior Angles:
SWBAT: Find measures of interior and exterior angles of polygons.
Exterior Angles:
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
e= Measure of each Exterior Angle
n= # of sides
SWBAT: Find measures of interior and exterior angles of polygons.
Example 4:
Calculating the measure of an exterior angle given the number of sides or Vice Versa
Find the measure of each exterior angle of a
polygon with 18 sides.
e= ?
n= 18
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
𝒆 𝟑𝟔𝟎
=
𝟏
𝟏𝟖
𝟏𝟖𝒆 = 𝟑𝟔𝟎
𝒆 = 𝟐𝟎°
SWBAT: Find measures of interior and exterior angles of polygons.
YOU TRY IT:
Calculating the measure of an exterior angle given the number of sides or Vice Versa
The measure of an exterior angle of a convex regular
polygon is 45. Find the number of sides of the polygon.
e= 45°
n= ?
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
𝟒𝟓 𝟑𝟔𝟎
=
𝟏
𝒏
𝟒𝟓𝒏 = 𝟑𝟔𝟎
𝒏=𝟖
SWBAT: Find measures of interior and exterior angles of polygons.
YOU TRY IT:
Calculating the measure of an exterior angle given the number of sides or Vice Versa
How many sides does a regular polygon have if each
interior angle measures 160˚.
e= 20˚
n= ?
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
𝟐𝟎 𝟑𝟔𝟎
=
𝟏
𝒏
𝟐𝟎𝒏 = 𝟑𝟔𝟎
𝒏 = 𝟏𝟖
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 5: Solving Algebraic Problems (Pg 7)
FIND THE VALUE OF x.
Step 1: Calculate the sum
Step 2: Use Sum to write an
of the interior angles equation to solve for x.
S=180(n-2)
(x+2)+(x-8)+(x+7)+(x-3)+(x+6)+(x-4) = 720
S=180(6-2)
S=180(4)
S=720°
6x = 720
x = 120
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 5: Solving Algebraic Problems (Pg 6)
FIND THE VALUE OF x.
42°
Exterior Angles = 360°
(x-20)+(x-10)+x+(x+14)+29+21+42 = 360
4x+76 = 360
4x = 284
x = 71
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons
SWBAT: Calculate Interior and Exterior Angles of Polygons