Five-Minute Check (over Lesson 11–4)
Then/Now
New Vocabulary
Example 1: Classify Polygons
Key Concept: Interior Angles of a Polygon
Example 2: Standardized Test Example
Example 3: Real-World Example: Measure of One
Interior Angle
Example 4: Find Tessellations
Over Lesson 11–4
Find the value of x.
A. 128
B. 126
C. 124
D. 122
Over Lesson 11–4
Find the value of x.
A. 80
B. 60
C. 40
D. 20
Over Lesson 11–4
Classify the quadrilateral.
A. cube
B. parallelogram
C. rhombus
D. quadrilateral
Over Lesson 11–4
Classify the quadrilateral.
A. square
B. parallelogram
C. rhombus
D. quadrilateral
Over Lesson 11–4
Which statement best describes a trapezoid?
A. a parallelogram with exactly
one pair of parallel sides
B. a quadrilateral with exactly
one pair of parallel sides
C. a parallelogram with at least
two congruent sides
D. a quadrilateral with at least
two congruent sides
You have already classified quadrilaterals.
(Lesson 11–4)
• Classify polygons.
• Determine the sum of the measures of the
interior angles of a polygon.
• polygon
• diagonal
• interior angle
• regular polygon
• tessellation
Classify Polygons
Determine whether the figure is a
polygon. If it is, classify the
polygon. If it is not a polygon,
explain why.
The figure has 5 sides that only intersect at their
endpoints.
Answer: It is a pentagon.
Classify the polygon.
A. pentagon
B. hexagon
C. heptagon
D. octagon
Find the sum of the measures of the interior angles of
a heptagon.
A. 1260°
B. 1080°
C.
900°
D. 1620°
Read the Test Item
The sum of the measures of the interior angles is
(n – 2)180. Since a heptagon has 7 sides, n = 7.
Solve the Test Item
(n – 2)180 = (7 – 2)180
Replace n with 7.
= 5 ● 180
Simplify.
= 900
Multiply.
The sum of the measures of the interior angles of a
heptagon is 900°.
Answer: The answer is C.
What is the sum of the interior angles of an octagon?
A. 540°
B. 720°
C. 900°
D. 1080°
Measure of One Interior Angle
TRAFFIC SIGNS A stop sign is a regular octagon.
What is the measure of one interior angle in a stop
sign?
Step 1 Find the sum of the measures of the angles.
An octagon has 8 sides. Therefore, n = 8.
(n – 2)180 = (8 – 2)180
= 6(180) or 1080
Replace n with 8.
Simplify.
The sum of the measures of the interior angles is 1080°.
Measure of One Interior Angle
Step 2 Divide the sum by 8 to find the measure of
one angle.
1080 ÷ 8 = 135
Answer: So, the measure of one interior angle in a
stop sign is 135°.
PICNIC TABLE A picnic table in the park is a
regular hexagon. What is the measure of one
interior angle in the picnic table?
A. 720°
B. 128.57°
C. 120°
D. 108°
Find Tessellations
Determine whether or not a tessellation can be
created using only regular decagons. If not, explain.
The measure of each interior angle of a regular
decagon is 144°.
The sum of the measures of the angles where the
vertices meet must be 360°. So, solve 144°n = 360.
144n = 360
Write the equation.
Divide each side by 144.
Find Tessellations
n = 2.5
Simplify.
Answer: Since 360 is not evenly divisible by 144, it
cannot be used to make a tessellation.
Which regular polygon cannot be used to create a
tessellation?
A. hexagon
B. pentagon
C. quadrilateral
D. triangle