Pre-Algebra

5.4

Polygons

1. How many sides does a hexagon have?

2. How many sides does a pentagon have?

3. How many angles does an octagon have?

4. Evaluate (n – 2)180 for n = 7.

6

5

8

900

Warm Up

Learn to classify and find angles in polygons.

polygon

regular polygon

trapezoid

parallelogram

rectangle

rhombus

square

Vocabulary

The cross section of a brilliant-cut diamond is a pentagon. The most beautiful and valuable diamonds have precisely cut angles that maximize the amount of light they reflect.

A polygon is a closed plane figure formed by three or more segments. A polygon is named by the number of its sides.

nn-gon

8Octagon

7Heptagon

6Hexagon

5Pentagon

4Quadrilateral

3Triangle

Number of SidesPolygon

A. Find the sum of the angle measures in a hexagon.

4 • 180° = 720°

4 triangles

Divide the figure into triangles.

Example: Finding Sums of the Angle Measures in Polygons

B. Find the sum of the angle measures in a octagon.

6 • 180° = 1080°

6 triangles

Divide the figure into triangles.

Example: Finding Sums of the Angle Measures in Polygons Continued

A. Find the sum of the angle measures in a hexagon.

4 • 180° = 720°

4 triangles

Divide the figure into triangles.

Try This

B. Find the sum of the angle measures in a heptagon.

5 • 180° = 900°

5 triangles

Divide the figure into triangles.

Try This

The pattern is that the number of triangles is always 2 less than the number of sides. So an n-gon can be divided into n – 2 triangles. The sum of the angle measures of any n-gon is 180°(n – 2).

All the sides and angles of a regular polygon have equal measures.

Find the angle measures in the regular polygon.

6 congruent angles

6x = 180°(6 – 2)

6x = 180°(4)

6x = 720°

6x 6

720°6

=

x = 120°

Example: Finding the Measure of Each Angle in a Regular Polygon

Find the angle measures in the regular polygon.

4 congruent angles

4y = 180°(4 – 2)

4y = 180°(2)

4y = 360°

y = 90°

4y 4

360°4

=

Example: Finding the Measure of Each Angle in a Regular Polygon

Find the angle measures in the regular polygon.

5 congruent angles

5a = 180°(5 – 2)

5a = 180°(3)

5a = 540°

5a5

540°5

=

a = 108°

a°

a°a°

a°

a°

Try This

Find the angle measures in the regular polygon.

8 congruent angles

8b = 180°(8 – 2)

8b = 180°(6)

8b = 1080°

8b 8

1080° 8

=

b = 135°

b°

b°

b° b°

b°

b°

b°b°

Try This

quadrilateral

parallelogram

rectangle

rhombus

square

Four-sided polygon

2 pairs of parallel sides

4 right angles

4 congruent sides

4 congruent sides and 4 right angles

Give all the names that apply to the figure.

Example: Classifying Quadrilaterals

Give all the names that apply to the figure.

quadrilateral

parallelogram

rhombus

Four-sided polygon

2 pairs of parallel sides

4 congruent sides

Example: Classifying Quadrilaterals Continued

Give all the names that apply to the figure.

quadrilateral

parallelogram

rectangle

Four-sided polygon

2 pairs of parallel sides

4 right angles

A.

Try This

Give all the names that apply to the figure.

quadrilateral

Four-sided polygon

B.

Try This

1. Find the sum of the angle measures in a

quadrilateral.

2. Find the sum of the angle measures in a

hexagon.

3. Find the measure of each angle in a regular

octagon.

360°

720°

135°

Lesson Quiz: Part 1

4. Write all of the names that apply to the figure

below.

quadrilateral, rhombus, parallelogram

Lesson Quiz: Part 2