Angle Pairs, Angle Addition, Parallel Lines & Transversals

Angle Pairs, Angle Addition, Parallel Lines & Transversals

Dr. Tom Giles

Adjacent Angles

• 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

• 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

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

Supplementary Angles

Multiple Choice

What type of angles are these?

• Adjacent Angles

• Linear Pair

• Complementary Angles

• Supplementary Angles

• Vertical Angles

Angle Addition Postulate

Review:

Segment Addition Postulate

Multiple Choice

Find the missing segment length / encontrar la longitud del segmento que falta

• 24

• 6

• 9

• 15

Adjacent Angles

Share vertex and a side

Angle Addition Postulate

• Small angle + Small Angle = Big angle

• If you are missing a SMALL angle - subtract

• If you are missing the BIG angle - add

Multiple Select

If you are missing one of the SMALL angles, you should /

Si te falta uno de los ángulos PEQUEÑOS, debes:

• Add

• Subtract

Multiple Select

If you are missing the BIG angle you should /

Si te falta el ángulo GRANDE deberías:

• Add

• Subtract

Multiple Choice

 Find m∠FED 

•  8°

•  127°°  

•  63°

Multiple Choice

 Find m∠RSM

•  85°

•  195°  

•  55°

Multiple Choice

 Find m∠VUZ

•  22°

•  322° 

•  172°

Multiple Choice

 Find m∠TSR  

•  18°

•  114°

•  100° 

Multiple Choice

 Find m∠CDT 

•  250° 

•  80°

•  90°

Multiple Choice

 Find m∠WVZ

•  43°

•  215°

•  86° 

Multiple Choice

 Find m∠TUK

•  123°

•  30°

•  63°

Parallel Lines

Parallel lines are on the same plane, but they never intersect.

Transversal

A line that intersects two or more coplanar lines at two different points

transversal line t

​This creates angles inside and outside the two original lines.

Interior Angles

Exterior Angles

​

​The angles on the left are equal pairs.

​The angles on the right are pairs that add up to 180^o.

Multiple Choice

Which of these is the name of the angles on opposite sides of the transversal and outside of the parallel lines?

• Alternate Interior Angles

• Vertical Angles

• Alternate Exterior Angles

• Same-Side Int Exterior Angles

Multiple Choice

Angles on the same side of the transversal and in corresponding positions are called...

• Linear Pair

• Alternate Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

Multiple Choice

What is the relationship between angles A and B?

• Corresponding

• Alternate Interior

• Alternate Exterior

• Supplementary

Multiple Choice

What is the relationship between angles A and B?

• Corresponding

• Alternate Exterior

• Alternate Interior

• Supplementary

Multiple Choice

What is the relationship between angles A and B?

• Corresponding

• Alternate Exterior

• Alternate Interior

• Supplementary

Multiple Choice

If m∠6 = 59, what is m∠3?

• 118

• 121

• 59

• 180

Multiple Choice

If m∠2 = 60, what is m∠4?

• 180

• 120

• 60

• 30

Multiple Choice

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

• $$\angle1$$  

• $$\angle5$$  

• $$\angle3$$  

• $$\angle6$$  

• $$\angle9$$  

Multiple Choice

Given the following two parallel lines cut by a transversal.

Which pair of angles represent corresponding angles?

• $$\angle1$$  and  $$\angle6$$  

• $$\angle6$$  and $$\angle5$$  

• $$\angle7$$  and $$\angle8$$  

• $$\angle4$$  and $$\angle8$$  

Multiple Choice

Given the following two parallel lines cut by a transversal.

Which pair of angles represent alternate interior angles?

• $$\angle3$$  and $$\angle8$$  

• $$\angle7$$  and $$\angle2$$  

• $$\angle7$$  and $$\angle8$$  

• $$\angle4$$  and $$\angle8$$  

Multiple Choice

If the  $$m\angle1\ =\ 57\degree,$$  find the measure of  $$\angle5$$ ?

• $$123\degree$$  

• $$57\degree$$  

• $$180\degree$$  

• Cannot be determined