Over Lesson 11–4

A. AB. BC. CD. D

A. 80

B. 60

C. 40

D. 20

Find the value of x.

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

A simple closed figure in a plane formed by three or more line segments

A line segment that joins two nonconsecutive vertices of a polygon

An angle formed inside of a polygon

A polygon having all sides congruent and all angles congruent

Side Number Name3 Triangle4 Quadrilateral5 Pentagon6 Hexagon7 Heptagon8 Octagon9 Nonagon10 Decagonn n-gon

Polygon Names

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. AB. BC. CD. D

A. pentagon

B. hexagon

C. heptagon

D. octagon

Classify the polygon.

Find the sum of the measures of the interior angles of a heptagon.

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 900°

A. AB. BC. CD. D

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. AB. BC. CD. D

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?