Geometry CPE
Name: _______________
HOMEWORK: Interior + Exterior angles of POLYGONS
Date: _______________
Directions: Please complete the following. Show all work!
1. What is the polygon angle sum theorem? What is it used for?
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2. How can you find the measure of one interior angle of a regular polygon if you are given the number of
sides of the polygon? What if you are given the interior angle sum of the polygon?
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3. Explain the difference between a polygon and a regular polygon.
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What is the sum of the interior-angle measures of a:
a. Nonagon:
b. 27-gon:
c. 50-gon:
How many sides are on a polygon whose sum of interior-angle measures is:
d. 12960°
e. 2340°
f.
6568,020°
How many sides are on a REGULAR polygon with the given angle measure?
a. Interior: 165° b. Exterior: 1.25°
c. Interior: 179.25°
d. Exterior: 20°
Find the measure of an interior angle and an exterior angle of a REGULAR polygon with the given trait.
Interior angle
a. 13 sides
b. Sum of interior angle measures: 4500°
c. 45 sides
d. Sum of interior angle measures: 3420°
Exterior angle
Find the sum of the interior-angle measures of a REGULAR polygon with the given trait:
a. Interior-angle measure: 178.8°
(1) Number of sides: ________________
(2) Sum of interior-angle measures: ____
b. Exterior-Angle measure: 1.8°
(1) Number of sides: ________________
(2) Sum of interior-angle measures: ____
Find the value for x.
Find the value of x.
5.
1.
2.
3.
4.
In the figure below, m∠1 = (8x + 2)o, m∠2 = (x – 20)o, m∠3 = (6x + 7)o, m∠4 = (3x + 1)o,
and m∠5 = (-3x + 100)o. Find x. Then find m∠5.
Find the value of x.
5.
1.
2.
3.
4.
In the figure below, m∠1 = (8x + 2)o, m∠2 = (x – 20)o, m∠3 = (6x + 7)o, m∠4 = (3x + 1)o,
and m∠5 = (-3x + 100)o. Find x. Then find m∠5.