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
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