Linear Pairs and Vertical Angles Assignment and Quiz

What is the value of m?

10

What is the value of x?

20

What is m∠SRW?

126

What is the value of x? (assignment)

45

What is the measure of ∠DAE?

45°

mSRW = __°

95

In which diagram are angles 1 and 2 vertical angles?

A

In the diagram, which angles are vertical angles? Check all that apply.

ABE and CBD ABC and EBD

Which angle is a vertical angle with EFD?

AFB

Which are vertical angles?

AFE and BFD

In the diagram, which angle is part of a linear pair and part of a vertical pair?

EFA

Marcus states that angle ORP and angle LRP are a linear pair. Which best describes his statement?

He is incorrect. Ray RO and ray RL are not opposite rays.

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.

If you know the measure of one angle in a linear pair, you can find the measure of the other because the sum of the measure of the two angles is 180 degrees. If you know the measure of one angle in a pair of vertical angles, you can find the measure of the other because they are congruent.

Given: mEDF = 120°; mADB = (3x)°; mBDC = (2x)° Prove: x = 24 What is the missing reason in step 3?

NOT definition of congruency

Given: mORP = 80° mORN = (3x + 10)° Prove: x = 30 Which statement could be used in step 2 when proving x = 30?

ORP and ORN are a linear pair

Given: mADE = 60° and mCDF = (3x + 15)° Prove: x = 15 What is the missing statement and the missing reason in step 5?

Statement: 60 = 3x + 15; Reason: substitution

Which pair of angles are vertical angles?

WRS and VRT

Given: m∠ELG = 124° Prove: x = 28 Complete the steps in the two-column proof.

angle addition postulate 2x = 56

If the m∠SRW = 85°, what are the measures of ∠VRU and ∠URW? m∠VRU = __° m∠URW = __°

m∠VRU = 80° m∠URW = 15°

Given: m∠QVR = 49° Prove: x = 15 Complete the steps of the proof.

vertical angles theorem 3x + 4 = 49

Which angles are linear pairs? Check all that apply.

∠SRT and ∠TRV ∠VRW and ∠WRS ∠VRU and ∠URS

Which is a pair of vertical angles?

∠TRS and ∠VRW