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NAME
DATE
4-2
PERIOD
Study Guide and Intervention
Angles of Triangles
Triangle Angle-Sum Theorem If the measures of two angles of a triangle are
known, the measure of the third angle can always be found.
Triangle Angle Sum
Theorem
B
The sum of the measures of the angles of a triangle is 180.
In the figure at the right, m∠A + m∠B + m∠C = 180.
A
Example 1
Example 2
Find the missing
angle measures.
Find m∠T.
S
B
35°
90°
T
A
m∠R + m∠S + m∠T = 180
58°
1
C
2
Triangle Angle -
Substitution
3
D
E
Sum Theorem
25 + 35 + m∠T = 180
60 + m∠T = 180
m∠T = 120
108°
m∠1 + m∠A + m∠B = 180
Triangle Angle - Sum
Theorem
Simplify.
m∠1 + 58 + 90 = 180
m∠1 + 148 = 180
m∠1 = 32
Subtract 60 from
each side.
Substitution
Simplify.
Subtract 148 from
each side.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
m∠2 = 32
Vertical angles are
congruent.
m∠3 + m∠2 + m∠E = 180
Triangle Angle - Sum
Theorem
m∠3 + 32 + 108 = 180
m∠3 + 140 = 180
m∠3 = 40
Substitution
Simplify.
Subtract 140 from
each side.
Exercises
Find the measures of each numbered angle.
1.
62°
3. V
60°
W
U
5.
90°
1
P
2
M
2.
S
1
Q
N
4. M
1
30°
T
30°
R
66°
1
58°
Q
2
3
N
50°
O
P
R
6. A
1 2
T 60°
W
Chapter 4
30°
20°
152°
G
S
11
1
D
Glencoe Geometry
Lesson 4-2
25°
R
C
NAME
DATE
4-2
PERIOD
Study Guide and Intervention
(continued)
Angles of Triangles
Exterior Angle Theorem
At each vertex of a triangle, the angle formed by one side
and an extension of the other side is called an exterior angle of the triangle. For each
exterior angle of a triangle, the remote interior angles are the interior angles that are not
adjacent to that exterior angle. In the diagram below, ∠B and ∠A are the remote interior
angles for exterior ∠DCB.
Exterior Angle
Theorem
The measure of an exterior angle of a triangle is equal to
the sum of the measures of the two remote interior angles.
m∠1 = m∠A + m∠B
Example 1
Find m∠1.
Example 2
S
1
D
A
C
Find x.
P
80°
R
B
78° Q
1
60°
T
x°
S
m∠1 = m∠R + m∠S
= 60 + 80
= 140
Exterior Angle Theorem
Substitution
Simplify.
55°
R
m∠PQS = m∠R + m∠S
78 = 55 + x
23 = x
Exterior Angle Theorem
Substitution
Subtract 55 from each
side.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises
Find the measures of each numbered angle.
X
1.
A
2.
35°
50°
Y
1
65°
Z
3.
W
N
1
3
Q
O
M
60°
2
2 1
25°
B
C
S
R
4.
80°
V
1
60°
3
2
35°
U
P
D
36°
T
Find each measure.
5. m∠ABC
6. m∠F
A
E
95°
B
2x°
Chapter 4
x°
145°
C
58°
D
H
12
x°
G
F
Glencoe Geometry