Download Lesson 8-1 Angles of Polygons

Lesson 8-1 Angles of Polygons
• Theorem 8.1 Interior Angle Sum Theorem
If a convex polygon has n sides and S is the sum
of the measures of its interior angles, then
S = 180(n – 2)
• Theorem 8.2 Exterior Angle Sum Theorem
If a polygon is convex, then the sum of the
measures of the exterior angles, one at each
vertex, is 360.
ARCHITECTURE A mall
is designed so that five walkways
meet at a food court that is in the
shape of a regular pentagon. Find
the sum of measures of the interior
angles of the pentagon.
Since a pentagon is a convex polygon, we can use the Angle Sum Theorem.
Interior Angle Sum Theorem
Simplify.
Answer: The sum of the measures of the angles is 540.
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.
Answer: 1080
The measure of an interior angle of a regular polygon is 135. Find the
number of sides in the polygon.
Use the Interior Angle Sum Theorem to write an equation to solve for n, the
number of sides.
Interior Angle Sum Theorem
Distributive Property
Subtract 135n from each side.
Add 360 to each side.
Divide each side by 45.
Answer: The polygon has 8 sides.
The measure of an interior angle of a regular polygon is 144. Find the
number of sides in the polygon.
Answer: The polygon has 10 sides.
Find the measure of each interior angle.
Since
the sum of the measures of the interior angles is
Write an equation to express the sum of the measures of the interior angles
of the polygon.
Sum of measures of angles
Substitution
Combine like terms.
Subtract 8 from each side.
Divide each side by 32.
Use the value of x to find the measure of each angle.
Answer:
Find the measure of each interior angle.
Answer:
Find the measures of an exterior angle and an interior angle of convex
regular nonagon ABCDEFGHJ.
At each vertex, extend a side to form one exterior angle.
The sum of the measures of the exterior angles is 360. A convex regular
nonagon has 9 congruent exterior angles.
Divide each side by 9.
Answer: The measure of each exterior angle is 40. Since each exterior angle
and its corresponding interior angle form a linear pair, the
measure of the interior angle is 180 – 40 or 140.
Find the measures of an exterior angle and an interior angle of convex
regular hexagon ABCDEF.
Answer: 60; 120