Vertical Angles and Linear Pairs

Review & Practice: Angle Pairs

Vocab:

congruent- same measure (or equivalent)

complimentary- adds to 90

supplementary- adds to 180

Adjacent Angles (not always congruent, just next to each other)

• Two angles that lie in the same plane and have a common vertex and a common side but no common interior points

• Two angles that are next to each other

Linear Pair= Supplementary = adds to 180

• A pair of adjacent angles with noncommon sides that are opposite rays

• Notice that the first 4 letters of linear spell line, so a linear pair forms a line.

Multiple Choice

Find the value of x in the diagram so that the angles form a linear pair

• 118

• 62

• 72

• 68

Multiple Choice

• x = 118

• x = 108

• x = 28

• x = 58

• x = 62

Multiple Choice

Which angle is a linear pair with $$\angle1$$  ?

• $$\angle2$$  

• $$\angle3$$  

• $$\angle4$$  

• $$\angle5$$  

• $$\angle6$$  

Vertical Angles = Congruent

Multiple Choice

Which angle is a vertical angle to with $$\angle7$$  ?

• $$\angle1$$  

• $$\angle5$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle9$$  

Multiple Choice

Find the missing angle.  Find x.

• 20^o

• 70^o

• 160^o

• 180^o

Multiple Choice

Which angles are vertical angles?

• $$\angle8\ \ and\ \angle7$$

• $$\angle8\ and\ \angle6$$

• $$\angle8\ and\ \angle5$$

Complementary Angles = add to 90

Supplementary Angles = add to 180

Multiple Choice

What type of angles are these?

• Adjacent Angles

• Linear Pair

• Complementary Angles

• Supplementary Angles

• Vertical Angles

Other types of Angle Pairs

Alternate Interior Angles = congruent

Alternate Exterior Angles = congruent

Corresponding Angles = congruent

Same-Side Interior Angles = supplementary

Finding x.

Algebra time!

Multiple Choice

Given the following two parallel lines that have been cut by a transversal.

Which two angles would be Alternate Exterior?

• $$\angle8$$ and $$\angle2$$

• $$\angle6$$ and $$\angle3$$

• $$\angle5$$ and $$\angle4$$

• $$\angle5$$ and $$\angle1$$

Multiple Choice

Given the following two parallel lines cut by a transversal.

Which pair of angles represents alternate exterior angles?

• $$\angle4$$  and $$\angle8$$  
  

• $$\angle7$$  and $$\angle5$$  
  

• $$\angle1$$  and  $$\angle2$$  
  

• $$\angle6$$  and  $$\angle5$$  
  

Multiple Choice

Given the following two parallel lines cut by a transversal.

Which pair of angles represents alternate interior angles?

• $$\angle3$$  and $$\angle8$$  
  

• $$\angle7$$  and $$\angle2$$  

• $$\angle7$$  and $$\angle8$$  

• $$\angle4$$  and $$\angle8$$  

Multiple Choice

Given the following two parallel lines cut by a transversal.

Which pair of angles represents corresponding angles?

• $$\angle1$$  and  $$\angle6$$  

• $$\angle6$$  and $$\angle5$$  

• $$\angle7$$  and $$\angle8$$  

• $$\angle4$$  and $$\angle8$$  

Multiple Choice

Given the two parallel lines cut by a transversal.

What is the vertical angle to  $$\angle4$$  ?

• $$\angle2$$  

• $$\angle6$$  
  

• $$\angle8$$  
  

• $$\angle7$$  
  

Multiple Choice

Supplementary angles add up to...

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

Multiple Choice

Complementary angles add up to...

• 45 degrees

• 90 degrees

• 180 degrees

• 360 degrees

Multiple Choice

$$Find\ m\angle6.$$  

• 45

• 60

• 90

• 120

Multiple Choice

Given $$m\angle1$$  is 105°, what is the  $$m\angle4?$$  

• $$85\degree$$  

• $$105\degree$$  

• $$115\degree$$  

• $$180\degree$$  

Fill in the Blanks

$Find\ the\ m\angle1.$  

Fill in the Blanks

Find the value of x.

Fill in the Blanks

Find the value of x.

Fill in the Blanks

$Find\ the\ m\angle1.$  

Multiple Select

Select all the pairs that are alternate exterior angles.

• ∠5 and ∠4

• ∠1 and ∠7

• ∠2 and ∠8

• ∠8 and ∠1

• ∠4 and ∠6

Multiple Select

Select all the pairs that are alternate interior angles.

• ∠5 and ∠4

• ∠6 and ∠5

• ∠2 and ∠8

• ∠8 and ∠1

• ∠3 and ∠5

Fill in the Blanks

What is the $m\angle3?$