Linear Pairs and Vertical Angles Answers

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1
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Which angles are linear pairs? Check all that apply.

A
∠SRT and ∠TRV
B
∠SRT and ∠TRU
C
∠VRW and ∠WRS
D
∠VRU and ∠URS
E
∠URW and ∠WRS
2
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What did you include in your response? Check all that apply.

A
The sum of the measures of the angles in a linear pair is 180 degrees.
B
Vertical angles are congruent.
109667

Complete the steps in the two-column proof.

Answers:
♣::linear pair postulate
♦::2x = 56
109669

definition of congruencedefinition of vertical anglesvertical angles theoremvertical angles form a line

A
definition of congruence
B
definition of vertical angles
C
vertical angles theorem
D
vertical angles form a line
109670

Which is a pair of vertical angles?

A
∠VRU and ∠SRT
B
∠TRS and ∠VRW
C
∠TRV and ∠WRU
D
∠WRV and ∠SRW
109672

Imagine two lines intersect. How can the properties of linear pairs and vertical angles help to determine the angle measures created by the intersecting lines? Explain.

Answer:

When two lines intersect, they form linear pairs and vertical angles. The angles in a linear pair are supplementary, meaning their measures add up to 180 degrees. Therefore, if you know the measure of one angle, you can find its linear pair by subtracting from 180. Vertical angles are congruent, so their measures are equal. By using these two properties, knowing just one angle measure allows you to determine the measures of all four angles created by the intersection.

109674

Which angles are linear pairs? Check all that apply.

A
∠SRT and ∠TRV
B
∠SRT and ∠TRU
C
∠VRW and ∠WRS
D
∠VRU and ∠URS
E
∠URW and ∠WRS
109675

Which is a pair of vertical angles?

A
∠VRU and ∠SRT
B
∠TRS and ∠VRW
C
∠TRV and ∠WRU
D
∠WRV and ∠SRW
109677

✔ 2x = 562x = 582x = 2042x = 304

A
✔ 2x = 56
B
2x = 58
C
2x = 204
D
2x = 304
109678

♣: [___]

A
addition property of equality
B
linear pair postulate
C
definition of congruence
D
definition of vertical angles
109680

Complete the steps of the proof.

Answers:
♣::vertical angles theorem
♦::3x + 4 = 49
109681

Complete the steps of the proof.

Answers:
♣::vertical angles theorem
♦::3x + 4 = 49
109682

3x + 4 = 15 ✔ 3x + 4 = 49measure of angle QVR = 49 degreesmeasure of angle UVT = (3x + 4) degrees

A
3x + 4 = 15
B
✔ 3x + 4 = 49
C
measure of angle QVR = 49 degrees
D
measure of angle UVT = (3x + 4) degrees
109684

510✔ 1520

A
5
B
10
C
✔ 15
D
20

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