Main Idea and New Vocabulary

Example 1: Classify Polygons

Example 2: Classify Polygons

Example 3: Find the Sum of the Angles of a Polygon

Key Concept: Interior Angle Sum of a Polygon

Example 4: Real-World Example

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

• polygon

• pentagon

• hexagon

• heptagon

• octagon

• nonagon

• decagon

• equilateral

• equiangular

• regular polygon

Classify Polygons

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

Answer: The figure is not a polygon because it has

a curved side.

A. yes; octagon; regular

B. yes; octagon; not regular

C. yes; hexagon; regular

D. not a polygon; not closed

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

Classify Polygons

The figure has 5 congruent sides and 5 congruent angles.

Answer: The figure is a regular pentagon.

A. yes; quadrilateral; regular

B. yes; quadrilateral; not regular

C. yes; pentagon; not regular

D. not a polygon; not closed

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

Find the Sum of the Angles of a Polygon

Find the sum of the angle measures of an 11-sided polygon.

Draw all of the diagonals from one vertex as shown and count the number of triangles formed.

Answer: So, the sum of the angle measures of an

11-sided polygon is 1,620°.

Find the sum of the angle measures in the polygon.

9 × 180° = 1,620°

A. 720°

B. 900°

C. 1080°

D. 1,260°

Find the sum of the angle measures of a 7-sided polygon.

PATTERNS Ms. Pena is creating a stencil for a design she is drawing on a wall. She wants the stencil to be a regular hexagon. She needs to know the measure of each angle before she can make her stencil. Find each angle measure of a regular hexagon.

Step 1 Find the sum of the measures of the angles.

S = (n – 2)180 Write the formula.

S = (6 – 2)180 Replace n with 6.

S = (4)180 or 720 Simplify.

The sum of the measures of the angles is 720°.

Step 2 Divide 720 by 6, the number of interior angles,to find the measure of one angle. So, themeasure of one angle of a regular hexagon is720 6 or 120.

Answer: Each angle of a regular hexagonmeasures 120°.

A. 1,440°

B. 1,080°

C. 180°

D. 135°

PAINTING Harry is painting a picture of a street and wants to include a stop sign in the shape of an octagon. He wants to know the measure of each angle to help him get the proportions correct. Find the measure of each angle of a regular octagon.