Page 10 - Math Course 3 (Book 2)

Sum of the Angles of a Polygon
Mo. 7

Lesson 1
Let’s Begin

KEY CONCEPTS:
Interior Angles of Regular Polygons
1. Find the sum of the measures of the
interior angles of a polygon.
2. Find the sum of the measures of the Example
exterior angles of a polygon

ARCHITECTURE
MO. 7 - L1a A mall is designed so that five walkways meet at a
food court that is in the shape of a regular penta-
Sum of the Angles of a gon. Find the sum of the measures of the interior

Polygon angles of the pentagon.

Vocabulary A-Z Since the pentagon is a Food
convex polygon, we can
Let us learn some vocabulary use the Interior Angle Court
Sum Theorem.
diagonal

A line segment connecting non-adjacent vertices
of a polygon. S = 180(n – 2) Interior Angle Sum Theorem

= 180(5 – 2) n = 5

= 180(3) or 540 Simplify.
Diagonal

The sum of the measures of
Answer
the angles is 540.

THEOREM 7.1 Sides of a Polygon

Interior Angle Sum Example

If a convex polygon has n sides and S is the sum of
the measures of its interior angles, then
S = 180(n – 2) The measure of an interior angle of a regular
polygon is 135. Find the number of sides in the
Example: polygon.
n = 5
S = 180(n – 2) Use the Interior Angle Sum Theorem to write an
= 180(5 – 2) or 540 equation to solve for n, the number of sides.

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