Finding Measures of Interior and Exterior Angles of Polygons, Study notes of Analytical Geometry and Calculus

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Angles in polygons

Day 1

Read Page 1 And Complete Questions at The bottom:

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

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

13 = 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°

Each Angle 90°

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

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 = -

n = 18

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 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.