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-