8.7-Describe Angle Relationships in Triangles

​8.7 Describe Angle Relationships

By Jessica Freeman

Let's take a second to review what we just learned.

The following six slides will review your understanding of angle relationships when a transversal cuts through a set of parallel lines
.
Congruent Relationships (set up angle expressions = to each other): Vertical Angles, corresponding angles, alternate interior angles, and alternate exterior angles

Supplementary Relationships (combine angle expressions AND set up = 180): linear pairs, same-side interior angles, and same-side exterior angles

Multiple Choice

∠1 and ∠3 can best be described as -

• complementary angles
• supplementary angles
• vertical angles
• adjacent angles

Multiple Choice

What are supplementary angles?

• Angles that add up to 180°
• Angles that add up to 90°
• Angles that are equal to each other
• Angles that are opposite of each other when lines intersect

Multiple Choice

Solve for x

• 6
• 140
• 20
• 90

Multiple Choice

Which pair of angles are alternate exterior angles?

• Angle 7 and Angle 4
• Angle 2 and Angle 6
• Angle 8 and Angle 1
• Angle 2 and Angle 8

Multiple Choice

What is the value of x?

• -6
• 22
• 16
• 21

Multiple Choice

What is the measure of ∠ABC?

• 25°
• 75°
• 108°
• 150°

Fill in the Blanks

What is the measure of angle Z $\degree$  ?

Poll

How do you feel about finding the missing angle when given 2 angles?

• I need more help with this

• I understand some of this

• I got this

• I could teach it to others

Multiple Choice

Which equation can be use to solve for X?

• $$4x+20=2x$$

• $$4x+20\ -2x\ -2x=180$$

• $$4x\ -20+2x=2x$$

• $$4x-20+2x+2x=180$$

Multiple Choice

Which equation can be use to solve for X?

• $$6x+1=13x-3$$

• $$6x+1+13x+3=68$$

• $$68+6x+1+13x-3=180$$

• $$68=13x-3$$

Multiple Choice

Solve for the missing variable.

• m<x = 43

• m<x = 57

• m<x = 123

• m<x = 47

Multiple Choice

Solve for the missing angle.

• m<y = 111

• m<y = 26

• m<y = 85

• m<y = 154

Multiple Choice

Solve for the missing angle.

• m<x = 75

• m<x = 42

• m<x = 63

• m<x = 105

Multiple Choice

Solve for the missing variable.

• x = 60

• x = 50

• x = 34

• x = 20

Multiple Choice

Find the value of x.

• A

• B

• C

• D

Multiple Choice

What is the measure of angle B?

• 47°

• 57°

• 46°

• 58°

Multiple Choice

Find the measure of the indicated angle. 

• 80
• 58
• 42
• 138

​HINT: reference the last part of the lesson objective/purpose on slide 1

Multiple Choice

Find the measure of the indicated angle. 

• 40
• 108
• 72
• 68

Multiple Choice

Use the relationship between the exterior angle and its remote interior angles to find m<CBA.

• 3 degrees
• 70 degrees
• 50 degrees
• 7 degrees

Multiple Choice

Use the relationship between the exterior angle and its remote interior angles to find m<CBA.

• 3 degrees
• 70 degrees
• 50 degrees
• 7 degrees

Multiple Choice

What is the measure of angle b?

• 36^o
• 56^o
• 63^o
• 117^o

Multiple Choice

Find the measure of the indicated angle. 

• 145
• 113
• 102
• 78

Multiple Choice

Find the measure of the indicated angle. 

• A
• B
• C
• D

Multiple Choice

What is the measure of angle B?

• 47°

• 57°

• 46°

• 58°

Multiple Choice

Find the measure of the missing angle.

• 105 degrees

• 25 degrees

• 80 degrees

• 75 degrees

Multiple Choice

What is the measure of angle b?

• 36^o
• 56^o
• 63^o
• 117^o

Multiple Choice

Find the value of x by using the exterior angle theorem.

• A
• B
• C
• D

Multiple Choice

Find side length X.

• 30
• 25
• 15
• 40

Multiple Choice

If two figures are similar, the corresponding sides are ______________.

• equal
• congruent
• proportional
• none of these

Multiple Choice

Are the following similar? Why or why not?

• Yes. All pairs of corresponding angles are congruent.
• No, the corresponding angles are not equal.
• No, the ratios of the corresponding sides are not equal.

Multiple Choice

Find the value of y.

• 24

• 16

• 6

• 54

Multiple Choice

Sides in similar figures must be proportional.  

• True
• False 

Multiple Choice

Matching sides are called

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Sides

Multiple Choice

What angle corresponds with A? 

• D
• F
• C
• E

Multiple Choice

Mrs. Ashley used similar triangles to make a design.  Which statement about the triangles in the design must be true?

• They are the same size and shape.
• They are the same size but different shapes.
• They have corresponding angles that are congruent.
• They have corresponding sides that are congruent.

Multiple Choice

If two figures are similar their angles are______.

• proportional
• congruent
• supplementary
• complementary

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

Which triangles are similar to triangle A?

• B
• C
• Both
• None

Multiple Choice

Are the following similar? Why or why not?

• Yes. All pairs of corresponding angles are congruent.
• No, the corresponding angles are not equal.
• No, the ratios of the corresponding sides are not equal.

Multiple Choice

Given that Triangle ABC is similar to Triangle DEF. Find the angle B.

• 60⁰

• 42⁰

• 79⁰

• 180⁰

Multiple Choice

Given that Triangle BAC is similar to Triangle EDF. Find the angle EFD.

• 45

• 22

• 113

• 18

Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary 

Multiple Choice

Matching angles are called

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Angles

Multiple Choice

All angles in similar figures are congruent.  

• True
• False

Multiple Choice

Are triangle ABC and triangle DEF similar?

• No

• Yes

Multiple Choice

The triangle sum theorem states that the sum of the interior angles of all triangles equals ________.

• 100*

• 180*

• 90*

• 360*

Multiple Choice

What is the measure of the missing angle?

• 43

• 63

• 137

• 53

Multiple Choice

Find the value of x by using the exterior angle theorem. (Click on the picture to make it larger and see the answers).

• A (12º)

• B (8º)

• C (15º)

• D (9º)

Multiple Choice

Calculate m∠BAD

• 76°

• 124°

• 36°

• 26°

Multiple Select

Which angle relationships are supplementary (add to 180º)? Pick 2

• Corresponding

• Alternate Interior

• Same Side Exterior

• Linear Pair

Multiple Choice

What is the measure of angle b?

• 36^o
• 56^o
• 63^o
• 117^o

Multiple Choice

What is the measure of angle x?

• 45
• 60
• 65
• 75

Multiple Choice

What is the value of x?

• 8

• 18

• 10

• 5

Multiple Choice

Which triangles are similar to triangle A?

• B
• C
• Both
• None

Multiple Choice

Sides in similar figures must be proportional.  

• True
• False 

Multiple Choice

Two objects that are the same shape but not the same size are _______.

• Congruent
• Vertical
• Similar
• Complementary 

Multiple Choice

Matching angles are called

• Corresponding Sides
• Corresponding Angles
• The Same
• Congruent Angles

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

Are the triangles similar?

• Yes
• No

Multiple Choice

All angles in similar figures are congruent.  

• True
• False

Labeling

Label the angles with the correct measures.

Drag labels to their correct position on the image

180

140

138

150

Labeling

Label the angles with the correct measures.

Drag labels to their correct position on the image

14

15

73

83

Labeling

Label the angles with the correct measures.

Drag labels to their correct position on the image

63

40

55

33

Multiple Choice

Find the measure of angle S

• A

• B

• C

• D

Multiple Choice

What is the measure of angle x?

• 45
• 60
• 65
• 75