Basic Mathematics for College Students

772 Chapter 9 An Introduction to Geometry

1

2 • 180° = 360°

(a)

3 • 180° = 540°

(b)

4 • 180° = 720°

(c)

1 1

2

Quadrilateral Pentagon Hexagon

2

4

2

3 3

Sum of the Angles of a Polygon

The sum , in degrees, of the measures of the angles of a polygon with sides

is given by the formula

S(n2)180°

S n

EXAMPLE (^5) Find the sum of the angle measures of a 13-sided polygon.
StrategyWe will substitute 13 for in the formula and evaluate
the right side.
WHYThe variable represents the unknown sum of the measures of the angles of
the polygon.
Solution
This is the formula for the sum of the measures
of the angles of a polygon.
Substitute 13 for n,the number of sides.
Do the subtraction within the parentheses.
Do the multiplication.
The sum of the measures of the angles of a 13-sided polygon is 1,980°.

1,980°

(11)180°

S( 13 2)180°

S(n2)180°

S

n S(n2)180°

Self Check 5

Find the sum of the angle

measures of the polygon shown

below.

EXAMPLE (^6) The sum of the measures of the angles of a polygon is 1,080°.
Find the number of sides the polygon has.
StrategyWe will substitute 1,080° for in the formula and solve
for.
WHYThe variable represents the unknown number of sides of the polygon.
Solution
This is the formula for the sum of the measures
of the angles of a polygon.
Substitute 1,080° for S,the sum of the measures
of the angles.
Distribute the multiplication by 180°.
To isolate 180°n,add 360° to both sides.
Do the additions.
To isolate n,divide
both sides by 180°.
Do the division.
The polygon has 8 sides. It is an octagon.
8 n

1,440°

180 °



180°n

180 °

1,440°180°n

1,080° 360 °180°n360° 360 °

1,080°180°n360°

1,080°(n2)180°

S(n2)180°

n

n

S S(n2)180°

Self Check 6

The sum of the measures of the

angles of a polygon is 1,620°.

Find the number of sides the

polygon has.

Now TryProblem 41

Now TryProblem 33

180

 11

180

1800

1,980

8

180  1,440

 1 440

0

1,0

1

80

 360

1,440