Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 7
Name ____________________________________________ Date _________________ Period ______ Topic: Sum of Interior Angles of a Triangle & Exterior Angle Theorem Class Website: msgiwa1.weebly.com
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
Reteaching Parallel Lines and Triangles
Triangle Angle-Sum Theorem:The measures of the angles in a triangle add up to 180.
Problem
In the diagram at the right, △ACD is a right triangle. What are m∠1 and m∠2?
Step 1 m∠1 + m∠DAB = 90 Angle Addition Postulate
m∠1 + 30 = 90 Substitution Property
m∠1 = 60 Subtraction Property of Equality
Step 2 m∠1 + m∠2 + m∠ABC = 180 Triangle Angle-Sum Theorem
60 + m∠2 + 60 = 180 Substitution Property
m∠2 + 120 = 180 Addition Property of Equality
m∠2 = 60 Subtraction Property of Equality
ExercisesFind mj1.
1. 2. 3.
4. 5. 6.
Algebra Find the value of each variable.
7. 8. 9.
A
B
C
D
1 2
6030
1
34 1
351
75 54
59 1
50 50
1
33 28
1
6
11
127X
Y
Z ZYX
27 9536
ZYX
3218
72
Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 7
Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.
Name Class Date
In the diagram at the right, ∠1 is an exterior angle of the triangle. An exterior angle is an angle formed by one side of a polygon and an extension of an adjacent side.
For each exterior angle of a triangle, the two interior angles that are not next to it are its remote interior angles. In the diagram, ∠2 and ∠3 are remote interior angles to ∠1.
The Exterior Angle Theorem states that the measure of an exterior angle is equal to the sum of its remote interior angles. So, m∠1 = m∠2 + m∠3.
Problem
What are the measures of the unknown angles?
m∠ ABD + m∠BDA + m∠BAD = 180 Triangle Angle-Sum Theorem
45 + m∠1 + 31 = 180 Substitution Property
m∠1 = 104 Subtraction Property of Equality
m∠ABD + m∠BAD = m∠2 Exterior Angle Theorem
45 + 31 = m∠2 Substitution Property
76 = m∠2 Subtraction Property of Equality
ExercisesWhat are the exterior angle and the remote interior angles for each triangle?
10. 11. 12.
exterior: exterior: exterior:
interior: interior: interior:
Find the measure of the exterior angle.
13. 14. 15.
1
2
3
A
B D45 1 2
31
1
2
3 4
M N
O
P
J
K
ML
X45
70
T
U
VW
90
53E
F
GH
4671
Reteaching (continued)
Parallel Lines and Triangles
Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 7
Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 7
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9)
40°20°
39° ?
10)
60°
65°
35°
?
50°
11) 86°
?
36°
84°
12)
23°35°
27° ?
13)
85°
115°
155°
?
14)
35°20°
156° ?
15)
60°
45°
100°
?
68°
16)
75°
45°
68°
?
79°
-2-
Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 7
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Solve for
x
.
17)
54°
55°
x
+ 74
18)
60°70°
8
x
+ 2
19)
64°
27°
97 +
x
20)
60°80°
x
+ 51
Find the measure of angle A.
21)
84°
x
+ 59
x
+ 51
A
22)
x
+ 67
x
+ 37A
23)
130°
8
x
+ 4
3
x
− 6A
24)
80°
4
x
+ 17
x
+ 23
A
-3-
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