Page 11 - Math Course 3 (Book 2)

Sum of the Angles of a Polygon

Interior Angle Sum MO. 7 - L1b
s = 180(n – 2)
Theorem
(135) n = 180(n – 2) S = 135n Polygons:
Exterior Angle Sums
135n = 180n – 360 Distributive Property

Subtract 135n from each
0 = 45n – 360 THEOREM 7.2
side.
360 = 45n Add 360 to each side.
Exterior Angle Sum
8 = n Divide each side by 45. If a polygon is convex, then the sum of the
measure of the exterior angles, one at each vertex,
is 360.
Answer The polygon has 8 sides. 1 2

3
5
Your Turn! Example: 4

m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360
Interior Angles of Regular Polygons

A decorative window is designed to have the
shape of a regular octagon. Find the sum of the
measures of the interior angles of the octagon.

A. 1440 Let’s Begin
B. 1260
C. 1080
D. 900
Interior Angles of Nonregular Polygons

Example

Find the measure of each interior angle.

S T
Answer
(11x + 4)° 5x°
Sides of a Polygon

The measure of an interior angle of a regular 5x° (11x + 4)°
polygon is 144. Find the number of sides in the R U
polygon.
Since n =4 the sum of the measures of the interior
A. 12 angles is 180(4 – 2) or 360. Write an equation to
B. 9 express the sum of the measures of the interior
C. 11 angles of the polygon.
D. 10
Sum of
360 = m∠R + m∠S + m∠S + m∠T measures of
+ m∠U
angles

360 = 5x + (11x + 4) + 5x + (11x+4) Substitution

Combine like
Answer 360 = 32x + 8
terms.
3