Download Problem Solving 9-7

Name
LESSON
Date
Class
Problem Solving
9-7 Angle Measures in Triangles
Write the correct answer.
1. Sean builds a triangular pen for his
pet rabbits. Two of the angles in the
pen measure 48° and 71°. Write an
equation that you can use to find the
measure of the third angle. Then find
the measure of the third angle.
2. A carpenter cuts a piece of wood in
the shape of a right triangle. One of
the acute angles of the triangle
measures 12°. Write an equation that
you can use to find the measure of
the other acute angle. Then find the
measure of this angle.
3. The figure shows the side view of a
skateboard ramp. Find the unknown
angle measure.
4. The figure shows the
intersection of three
straight roads. Find the
unknown angle measure.
68°
139°
x
38°
x
The figure shows a bridge that is known as a Pennsylvania
truss. Use the figure for Exercises 5–7. Select the best answer.
6. Which equation can be used to find
the measure of the angle labeled b?
F 52° b 180°
G 52° 90° b 180°
H 52° 90° b
J 52° 180° 90° b
5. What is the measure of the angle
labeled a?
A 48°
C 59°
B 53°
D 121°
7. The angles labeled c and d are
congruent. What is the measure of
the angle labeled c?
A 18°
B 54°
C 72°
D 108°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
72°
a
79
52°
c
d
62
42°
b
Holt Mathematics
Problem Solving
9-7 Angle Measures in Triangles
Challenge
9-7 Tricky Triangles
LESSON
LESSON
Find the unknown angle measure x in each figure.
1.
2. Q is congruent
to R.
x
3.
P
78°
x
Q
60°
R
51°
31° 50°
44°
30°
36°
7. A is congruent
to B.
8.
x
51°
9.
39°
22°
x
136°
C
B
35°
18°
11.
71°
60°
12.
110°
134°
x
41°
63°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
101°
7. The angles labeled c and d are
congruent. What is the measure of
the angle labeled c?
A 18°
B 54°
C 72°
D 108°
64°
61
6. Which equation can be used to find
the measure of the angle labeled b?
F 52° b 180°
G 52° 90° b 180°
H 52° 90° b
J 52° 180° 90° b
5. What is the measure of the angle
labeled a?
A 48°
C 59°
B 53°
D 121°
x
53°
51°
65°
x
Holt Mathematics
a
72°
79
52°
c
42°
d
b
62
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
Holt Mathematics
Puzzles, Twisters & Teasers
9-7 Find the Measure
Reading Strategies
9-7 Analyzing Information
LESSON
LESSON
P
x
To find the unknown angle measure x
in this figure, you must use two steps.
Q
59°
Find the missing angle measure in each triangle. When you
have completed the problem, look at the blank lines at the
bottom of the page. Notice if any of the angle degrees of the
letters match the degrees under the blank lines. If they do, write
the letter of the angle on the line. The resulting message will be
the answer to the riddle.
140°
R S
Step 1
Find the measurement of ∠PRQ.
1.
1. To find the unknown angle measure y, what should you do
first?
D
70°
K
J
x°
T
V
x 45°
x°
33°
W
x 60°
M
6.
N
x 120°
7.
S
25°
F
60°
30°
Z
x
x°
U
50°
I
35°
115°
z 55°
Solving the equation gives mDEF 120°.
A
y°
z°
3. Explain how to use what you know to find the unknown angle
measure y.
R
87°
30°
C
C
35°
x 105°
Y
x°
DEF and the 60° angle are supplementary, so mDEF 60° 180°.
L
x 68°
y 62°
x ° 112°
L
Why do you like studying about volcanoes?
The sum of the angle measures in triangle DEF is 180°, so
I
25° 120° y 180°. Solving the equation gives y 35°.
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
x°
70°
x 40°
5.
Find the measure of DEF.
63
40°
F
60°
2. Explain how to do this first step.
x°
4.
E
y
3.
V
Step 2
Now find the unknown angle measure x.
The sum of the angle measures in triangle PQR is 180°, so 59° 40° x 180°.
59° 40° x 180°
99° x 180°
Add 59° and 40°.
99°
99°
Subtract 99° from both sides.
x 81°
Answer each question.
2.
x°
Step 2
Step 1
Find the unknown angle measure x.
Find the measure of PRQ.
PRQ and the 140° angle are supplementary.
That means 140° mPRQ 180.
140° mPRQ 180°
140°
140°
Subtract 140° from both sides.
mPRQ 40°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
x
The figure shows a bridge that is known as a Pennsylvania
truss. Use the figure for Exercises 5–7. Select the best answer.
4x 5x
68°
10.
139°
x
38°
x
A
x
4. The figure shows the
intersection of three
straight roads. Find the
unknown angle measure.
68°
55°
55°
78°
3. The figure shows the side view of a
skateboard ramp. Find the unknown
angle measure.
2x
x
90° 12° x 180°
61°
6.
x
3x
2. A carpenter cuts a piece of wood in
the shape of a right triangle. One of
the acute angles of the triangle
measures 12°. Write an equation that
you can use to find the measure of
the other acute angle. Then find the
measure of this angle.
48° 71° x 180°
138°
5. 2x
2x
1. Sean builds a triangular pen for his
pet rabbits. Two of the angles in the
pen measure 48° and 71°. Write an
equation that you can use to find the
measure of the third angle. Then find
the measure of the third angle.
x
78°
150°
4.
Write the correct answer.
60°
50°
Holt Mathematics
T ’
105°
S
A
L
A
V
A
F
U
N
55°
62°
68°
62°
45°
62°
60°
115°
120°
Copyright © by Holt, Rinehart and Winston.
All rights reserved.
110
64
Holt Mathematics
Holt Mathematics