Main Idea and New Vocabulary
NGSSS
Example 1: Classify Polygons
Key Concept: Interior Angle Sum of a Polygon
Example 2: Sum of Interior Angle Measures
Example 3: Real-World Example
Five-Minute Check

• Find the sum of the angle measures of a polygon and the measure of an interior angle of a regular polygon.
• polygon
• interior angle
• equiangular
• regular polygon

MA.8.G.2.3
Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons.

Classify Polygons
Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.
Answer: It is not a polygon because it has a curved side.

Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.
A.
yes; pentagon
B.
yes; hexagon
C.
yes; heptagon
D.
No; the segments do not intersect at their endpoints.

Sum of Interior Angle Measures
ALGEBRA Find the sum of the measures of the interior angles of a 13-gon.
S
S
= (
= ( n
13
– 2)180
– 2)180
Write an equation.
A 13-gon has 13 sides.
Replace n with 13.
S = (11)180 or 1,980 Simplify.
Answer: The sum of the measures of the interior angles of a 13-gon is 1,980 °.

ALGEBRA Find the sum of the measures of the interior angles of an 18-gon.
A.
160 °
B.
2,880 °
C.
3,060 °
D.
3,240 °

DESIGN A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon.

Step 1 Find the sum of the measures of the angles.
S = ( n – 2)180 Write an equation.
S = ( 5 – 2)180 Replace n with 6.
S = (3)180 or 540 Simplify.
The sum of the measures of the interior angles is 540 ° .

Step 2 Divide 540 by 5, the number of interior angles, to find the measure of one interior angle.
540 ÷ 5 = 108
Answer: The measure of one interior angle of a regular pentagon is 108 °.

ART An artist is creating a sculpture that is made up of regular decagons. Find the measure of an interior angle of a regular decagon.
A.
144 °
B.
225 °
C.
1,440 °
D.
1,800 °

Find the sum of the measures of the interior angles of a hexagon.
A.
120 °
B.
360 °
C.
720 °
D.
1,080 °

Find the sum of the measures of the interior angles of a nonagon.
A.
140 °
B.
1,080 °
C.
1,260 °
D.
1,620 °

Find the measure of one interior angle in a regular octagon. Round to the nearest tenth if necessary.
A.
120 °
B.
135 °
C.
180 °
D.
1,080 °

Find the measure of one interior angle in a regular 14-gon. Round to the nearest tenth if necessary.
A.
154.3
°
B.
180 °
C.
2,160 °
D.
2,520 °

Find the measure of one interior angle in a regular 56-gon. Round to the nearest tenth if necessary.
A.
173.6
°
B.
176.8
°
C.
186.7
°
D.
9,720 °

The following statements are true about triangle XYZ.
• The measure of each angle is evenly divisible by 20.
• m 
X is greater than m

Z.
• m 
Z is greater than m

Y.
• m 
Y + m

Z = m

X.
What are the angle measures of triangle XYZ?
A.
m

X = 120
°, m 
Y = 20
°, m 
Z = 40
°
B.
m

X = 120 °, m 
Y = 30 °, m 
Z = 30 °
C.
m

X = 130 °, m 
Y = 20 °, m 
Z = 30 °
D.
m

X = 110 °, m 
Y = 50 °, m 
Z = 20 °