Day 1 - White Plains Middle School · SWBAT: Find measures of interior and exterior angles of...

SWBAT: Find measures of interior and exterior angles of polygons. (HW Pg:8-10)

Angles in polygons Day 1


Read Page 1 And Complete Questions at The bottom:


Warm Up (Pg. 1)


Sum of Interior Angles in Polygons (Pg. 2)


Sum of Interior Angles in Polygons (Pg. 2)

S=180(n-2) S= Sum of interior angles n= # of sides


Example 1: Calculating the Sum of Interior Angles (Pg. 2)

Find the sum of the interior angles of a decagon.

S=180(n-2)

S=180(10-2)

S=180(8)

S=1440°

S= ? n= 10


YOU TRY IT! (Pg. 2)

S=180(n-2)

S=180(14-2)

S=180(12)

S=2160°

Find the sum of the interior angles of a 14-gon.

S= ? n= 14


S=180(n-2)

1980=180(n-2)

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

11 = n - 2

180 180

+2 = +2 13 = n


You Try It: (Pg. 3) Calculating the number of sides of a polygon given the sum of the interior angles

S= 3240° n= # of sides

The sum of the interior angles of a convex regular polygon measure 3240, how many sides does the polygon have?

S=180(n-2)

3240=180(n-2)

18 = n - 2

180 180

+2 = +2 20 = n


Example 3: (Pg. 4) Calculating the measure of each of interior Angle of any regular polygon

S= n=

What is the measure of each interior angle of a regular octagon?

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)


i = measure of each interior angle of a regular convex polygon n= # of sides


Example 3: (Pg. 4) Calculating the measure of each of interior Angle of any regular polygon

i = ? n = 8

What is the measure of each interior angle of a regular octagon?

i = 𝟏𝟖𝟎(𝒏−𝟐)

𝒏

i = 𝟏𝟖𝟎(𝟖−𝟐)

𝟖

i = 𝟏𝟎𝟖𝟎

𝟖

i = 135


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


You Try It: (Pg. 4) Calculating the measure of each of interior Angle of any regular polygon

i = 160 n= ?

How many sides does a regular polygon have if each interior angle measures 160?

i = 𝟏𝟖𝟎(𝒏−𝟐)

𝒏

160 = 𝟏𝟖𝟎(𝒏 −𝟐)

𝒏

160n = 180n - 360 -180n = -180n

-20n = -360

n = 18


Exterior Angles: (Pg. 5)


Exterior Angles: (Pg. 5)

𝒆

𝟏=

𝟑𝟔𝟎

𝒏

e= Measure of each Exterior Angle n= # of sides


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

𝟏=

𝟑𝟔𝟎

𝒏

𝒆

𝟏=

𝟑𝟔𝟎

𝟏𝟖

𝟏𝟖𝒆 = 𝟑𝟔𝟎

𝒆 = 𝟐𝟎°


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

𝟏=

𝟑𝟔𝟎

𝒏

𝒆

𝟏=

𝟑𝟔𝟎

𝟑𝟔

𝟑𝟔𝒆 = 𝟑𝟔𝟎

𝒆 = 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

𝟏=

𝟑𝟔𝟎

𝒏

𝟒𝟓

𝟏=

𝟑𝟔𝟎

𝒏

𝟒𝟓𝒏 = 𝟑𝟔𝟎

𝒏 = 𝟖


Example 5: Solving Algebraic Problems (Pg 7) FIND THE VALUE OF x.

S=180(n-2)

S=180(6-2)

S=180(4)

S=720°

(x+2)+(x-8)+(x+7)+(x-3)+(x+6)+(x-4) = 720

6x = 720

x = 120

Step 1: Calculate the sum of the interior angles

Step 2: Use Sum to write an equation to solve for x.


Example 5: Solving Algebraic Problems (Pg 6) FIND THE VALUE OF x.

Exterior Angles = 360°

(x-20)+(x-10)+x+(x+14)+29+21+42 = 360

4x+76 = 360

4x = 284

x = 71

42°


Summary (Pg 7)


Exit Ticket (Pg 7)

e= ? n= 8

Day 1 - White Plains Middle School · SWBAT: Find measures of interior and exterior angles of...

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