Polygons

Polygons

​Objectives

• ​Define polygons

• ​Names of polygons

• ​Find the sum of interior and exterior angles in polygons

• ​Use the sum of interior and exterior angles to find missing angles in polygons

​Polygon

​A polygon is a two-dimensional shape made up of straight lines, and the shape is closed.

​What's in a name?

​Poly means many

​gon means angles

​

​Polygon means many angles

TYPES AND NAMES OF POLYGONS​

​Regular Polygon

A regular polygon is EQUILATERAL

and

EQUIANGULAR

​Types of Polygons

​​Draw a table in your books with two columns. We will fill in the columns from the information in the upcoming video.

​

​Number of sides Name of Polygon

INTERIOR ANGLES IN POLYGONS​

Multiple Choice

What is the SUM of the angle measures in a nonagon (9 sides)?

• 1440°
• 900°
• 1080°
• 1260°

Multiple Choice

What is the SUM of the angle measures in a hexagon (6 sides)?

• 720°
• 1080°
• 600°
• 540°

Multiple Choice

What is the sum of the interior angles for a      24-gon

• 3960
• 360
• 15
• 4280

Multiple Choice

What is the name of a 7 sided polygon?

• hexagon
• heptagon
• octagon
• nonagon

FINDING MISSING ANGLES

Multiple Choice

Find the measure of the angle indicated. 

• 139°
• 66°
• 138°
• 116°

Multiple Choice

Find the measure of the missing angle.

• 90^o
• 10⁰
• 130^o
• 50^o

Solving for the missing angle!

• To solve for the missing angle follow these steps!

• 1) Count the number of sides on the polygon - here we have 5 sides (pentagon)

• 2) Use our formula for the sum of the interior angles - S = 180(n - 2) S = 180(5-2) = 540 degrees

• 3) Add up the existing angles - 87 + 105 + 135 + 92 = 419 degrees

• 4) Subtract the sum of the existing angles from the sum of the interior angles : 540 - 419 = 121 degrees

Multiple Choice

Find the missing angle.

• 75
• 85
• 100
• 45

Multiple Choice

Find the measure of the angle x.

• 105
• 115
• 65
• 75

Multiple Choice

Find the value of X

• 94
• 25
• 36
• 180

Multiple Choice

Find the measure of angle K.

• 9

• 97°

• 48°

• 79°

Finding n​

​Example

​The sum of the interior angles of a regular polygon is 1800.

​

​How many sides does the polygon have?

​

​Find the measure of each interior angle.

Multiple Choice

If the sum of the interior angles of a polygon equals 900°, how many sides does the polygon have? 

• 7
• 9
• 10
• 12

Multiple Choice

A polygon has a sum of interior angle measures equal to 1620°. How many sides does the polygon have?

• 9
• 11
• 13
• 7

Example!

Multiple Choice

What is the measure of ONE interior angle in a regular hexagon (6 sides)?

• 60°
• 80°
• 108°
• 120°

Multiple Choice

What is the measure of ONE interior angle in a regular pentagon (5-sides)?

• 90°
• 108°
• 120°
• 180°