Download Find the sum of the interior angle measures of

7. 15-gon
ANSWER: 24°
5-4 Polygons and Angles
Find the sum of the interior angle measures of
the polygon.
1. pentagon
A tessellation is a repetitive pattern of polygons
that fit together without overlapping and
without gaps between them. For the
tessellation, find the measure of each angle at
the circled vertex. Then find the sum of the
angles.
ANSWER: 540°
2. 11-gon
ANSWER: 1,620°
3. 13-gon
ANSWER: 1,980°
8. ANSWER: 90°, 120°, 150°; 360°
4. The soccer ball below consists of repeating regular
pentagons and hexagons. Find the measure of one
interior angle of a pentagon.
9. ANSWER: 108°
Find the measure of an exterior angle of each
regular polygon.
ANSWER: 60°, 90°, 90°, 120°; 360°
Find the value of x in the figure.
10. 5. decagon
ANSWER: 36°
6. 20-gon
ANSWER: 18°
ANSWER: 80
7. 15-gon
ANSWER: 24°
A tessellation is a repetitive pattern of polygons
that fit together without overlapping and
without gaps between them. For the
tessellation, find the measure of each angle at
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the circled
vertex.byThen
find the sum of the
angles.
11. Page 1
ANSWER: 130
ANSWER: 5-4 Polygons
and Angles
80
11. ANSWER: 130° and 28°
13. Persevere with Problems How many sides does a
regular polygon have if the measure of an interior
angle is 160°? Justify your answer.
ANSWER: = 160
18;
(n – 2)
180
180n –
360
20n
n
ANSWER: 130
12. Model with Mathematics Refer to the graphic
novel frame below. Find the measures of the two
missing angles using properties of quadrilaterals and
=
160n
=
160n
=
=
360
18
Multiplication Property
of Equality
Distributive Property
Properties of Equality
Division Property of
Equality
parallel lines.
14. Reason Inductively If the number of sides of a
polygon increases by 1, what happens to the sum of
the measures of the interior angles?
ANSWER: It increases by 180°.
15. Reason Inductively Devon drew a regular polygon
and measured one of its interior angles. Explain why
it is impossible for his angle measure to be 145°.
ANSWER: Regular decagons have equal angles measuring 144° and regular 11-sided polygons have angles measuring
147.27°. 145° is between these two values so it cannot be the interior angle measure of a regular
polygon.
Find the sum of the interior angle measures of
the polygon.
16. heptagon
ANSWER: 900°
ANSWER: 130° and 28°
17. 14-gon
13. Persevere with Problems How many sides does a
regular polygon have if the measure of an interior
angle is 160°? Justify your answer.
ANSWER: 18;
ANSWER: 2,160°
18. 24-gon
= 160
(n – 2) = 160n
Multiplication Property
180
of Equality
180n – = 160n
Distributive Property
360
20n - Powered
= 360
Properties of Equality
eSolutions Manual
by Cognero
n
= 18
Division Property of
Equality
ANSWER: 3,960°
Find the measure of one interior angle in the
regular polygon. Round to the nearest tenth if
necessary.
19. nonagon
Page 2
ANSWER: 140°
2,160°
18. 24-gon
ANSWER: 5-4 Polygons
and Angles
3,960°
Find the measure of one interior angle in the
regular polygon. Round to the nearest tenth if
necessary.
19. nonagon
ANSWER: 140°
25. 18-gon
ANSWER: 20°
26. The surface of the dome of Spaceship Earth in
Orlando consists of repeating equilateral triangles as
shown. Find the measure of each angle in each
outlined triangle. Then make a conjecture about the
interior angle measures in equilateral triangles of
different sizes.
20. decagon
ANSWER: 144°
21. 19-gon
ANSWER: 161.1°
22. 16-gon
ANSWER: 157.5°
Find the measure of an exterior angle of the
regular polygon.
23. nonagon
ANSWER: 40°
24. 12-gon
ANSWER: 30°
25. 18-gon
ANSWER: 20°
ANSWER: The measure of each angle in each outlined triangle
is 60°. If a triangle is equilateral, the measure of each
angle will be 60° regardless of the size of the triangle.
27. Justify Conclusions What is the sum of the interior
angles of nonregular hexagons? Explain your
reasoning to a classmate.
ANSWER: Sample answer: The sum of the interior angles will
still be 720° because even though the figures are not regular, they are still hexagons.
26. The surface of the dome of Spaceship Earth in
Orlando consists of repeating equilateral triangles as
shown. Find the measure of each angle in each
outlined triangle. Then make a conjecture about the
interior angle measures in equilateral triangles of
different sizes.
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28. After the first two folds of an origami paper design,
the paper is shaped like a square with two isosceles
triangles removed from two adjacent corners.
Page 3
Angles AED and BCD are congruent. Select the
correct values to complete the model below to find
ANSWER: Sample answer: The sum of the interior angles will
5-4 Polygons
and Angles
still be 720° because even though the figures are not regular, they are still hexagons.
28. After the first two folds of an origami paper design,
the paper is shaped like a square with two isosceles
triangles removed from two adjacent corners.
ANSWER: 2
∙
x
+
3
∙
90
=
540
m∠AED = 135°
29. Fill in each box to make each statement true.
a. The sum of the interior angle measures of a
quadrilateral is _________.
b. The sum of the interior angle measures of a(n)
_________ is 720°.
c. The sum of the interior angle measures of an
octagon is _________.
d. The sum of the interior angle measures of a(n)
_________ is 1,620°.
Angles AED and BCD are congruent. Select the
correct values to complete the model below to find
the measure of angle AED.
x
180
2
360
3
540
45
720
90
∙
+
∙
=
Classify the pair of angles as complementary,
supplementary, or neither.
30. angle 1: 35°
angle 2: 55°
What is m∠AED?
ANSWER: 2
∙
x
+
3
∙
90
ANSWER: a. The sum of the interior angle measures of a
quadrilateral is 360°.
b. The sum of the interior angle measures of a(n)
hexagon is 720°.
c. The sum of the interior angle measures of an
octagon is 1,080°.
d. The sum of the interior angle measures of a(n) 11gon is 1,620°.
=
540
ANSWER: complementary
m∠AED = 135°
29. Fill in each box to make each statement true.
a. The sum of the interior angle measures of a
quadrilateral is _________.
b. The sum of the interior angle measures of a(n)
_________ is 720°.
c. The sum of the interior angle measures of an
octagon is _________.
d. The sum of the interior angle measures of a(n)
_________ is 1,620°.
31. angle 1: 62°
angle 2: 108°
ANSWER: neither
Find the value of x in the triangle.
32. ANSWER: a. The sum of the interior angle measures of a
quadrilateral is 360°.
b. The sum of the interior angle measures of a(n)
hexagon is 720°.
c. The sum of the interior angle measures of an
octagon is 1,080°.
d. The sum of the interior angle measures of a(n) 11eSolutions
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gon is 1,620°.
Classify the pair of angles as complementary,
ANSWER: 51
33. Page 4
ANSWER: 5-4 Polygons
and Angles
51
33. ANSWER: 26
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