SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Angles in polygons
Day 1
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Read Page 1
And
Complete
Questions at
The bottom:
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Warm Up (Pg. 1)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Sum of Interior Angles in Polygons (Pg. 2)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Sum of Interior Angles in Polygons (Pg. 2)
S=180(n-2)
S= Sum of interior angles
n= # of sides
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 1: Calculating the Sum of Interior Angles (Pg. 2)
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. (HW Pg:8-10)
YOU TRY IT! (Pg. 2)
Find the sum of the interior angles of a 14-gon.
S= ?
n= 14
S=180(n-2)
S=180(14-2)
S=180(12)
S=2160°
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 2: (Pg. 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. (HW Pg:8-10)
You Try It: (Pg. 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 3240, how many sides does the polygon have?
S= 3240°
n= # of sides
S=180(n-2)
3240=180(n-2)
180 180
18 = n - 2
+2 =
+2
20 = n
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 3: (Pg. 4)
Calculating the measure of each of interior Angle of any regular polygon
What is the measure of each interior angle
of a regular octagon?
S=
n=
Each Angle 60°
3(60°) = 180°
Each Angle 90°
4(90°) = 360°
Each Angle 108°
5(108°) = 540°
Regular Polygon:
A polygon which
is equiangular
(all angles the
same measure)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
i = measure of each interior angle of a
regular convex polygon
n= # of sides
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 3: (Pg. 4)
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 =
𝟏𝟖𝟎(𝒏−𝟐)
𝒏
i =
𝟏𝟖𝟎(𝟖−𝟐)
𝟖
i =
𝟏𝟎𝟖𝟎
𝟖
i = 135
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
You Try It: (Pg. 4)
Calculating the measure of each of interior Angle of any regular polygon
What is the measure of each interior angle
of a regular 12-gon?
i = ?
n = 12
i =
𝟏𝟖𝟎(𝒏−𝟐)
𝒏
i =
𝟏𝟖𝟎(𝟏𝟐−𝟐)
𝟏𝟐
i =
𝟏𝟖𝟎𝟎
𝟏𝟐
i = 150
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
You Try It: (Pg. 4)
Calculating the measure of each of interior Angle of any regular polygon
How many sides does a regular polygon have
if each interior angle measures 160?
i = 160
n= ?
i =
160 =
𝟏𝟖𝟎(𝒏−𝟐)
𝒏
𝟏𝟖𝟎(𝒏 −𝟐)
𝒏
160n = 180n - 360
-180n = -180n
-20n = -360
n = 18
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Exterior Angles: (Pg. 5)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Exterior Angles: (Pg. 5)
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
e= Measure of each Exterior Angle
n= # of sides
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Example 4:
(Pg 5)
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. (HW Pg:8-10)
YOU TRY IT:
(Pg 5)
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 36 sides.
e= ?
n= 36
𝒆 𝟑𝟔𝟎
=
𝟏
𝒏
𝒆 𝟑𝟔𝟎
=
𝟏
𝟑𝟔
𝟑𝟔𝒆 = 𝟑𝟔𝟎
𝒆 = 𝟏𝟎°
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
YOU TRY IT:
(Pg 6)
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. (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: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Summary (Pg 7)
SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)
Exit Ticket (Pg 7)
e= ?
n= 8