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

A. 128

B. 126

C. 124

D. 122

Find the value of x.

Over Lesson 11–4

A. 80

B. 60

C. 40

D. 20

Find the value of x.

Over Lesson 11–4

A. cube

B. parallelogram

C. rhombus

D. quadrilateral

Classify the quadrilateral.

Over Lesson 11–4

A. square

B. parallelogram

C. rhombus

D. quadrilateral

Classify the quadrilateral.

Over Lesson 11–4

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

Which statement best describes a trapezoid?

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.

A. pentagon

B. hexagon

C. heptagon

D. octagon

Classify the polygon.

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.

Answer: The answer is C.

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°.

A. 540°

B. 720°

C. 900°

D. 1080°

What is the sum of the interior angles of an octagon?

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 Replace n with 8.

= 6(180) or 1080 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.

Answer: So, the measure of one interior angle in a stop sign is 135°.

1080 ÷ 8 = 135

A. 720°

B. 128.57°

C. 120°

D. 108°

PICNIC TABLE A picnic table in the park is a regular hexagon. What is the measure of one interior angle in the picnic table?

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

Answer: Since 360 is not evenly divisible by 144, it cannot be used to make a tessellation.

n = 2.5 Simplify.

A. hexagon

B. pentagon

C. quadrilateral

D. triangle

Which regular polygon cannot be used to create a tessellation?