Geometry - Linear Pairs and Vertical Angles

Linear Pairs and Vertical Angles

Angle Addition Postulate

• The measure of an angle created by two or more adjacent angles is equal to the sum fo the measures of the individual angles.

Angles

• Adjacent Angles: coplanar angles with a common side, a common vertex, and no common interior points

• Vertical Angles: opposite angles formed by two intersecting lines

• Congruent Angles: two angles that have the same measure

Linear Pairs

• Two adjacent angles whose noncommon sides are opposite rays

• Supplementary (add up to 180 degrees)

• When two lines intersect they form two sets of linear pairs

Multiple Choice

Two angles are adjacent and have measures of 67 degrees and 123 degrees. Do the two angles form a linear pair?

• yes

• no

Multiple Choice

Find the value of x. 

• 14
• 112
• 108
• 104

Multiple Choice

Are the angles shown vertical angles, a linear pair, or neither?

• vertical angles

• linear pair

• neither

Vertical Angles

• Opposite (nonadjacent) angles formed by two intersecting lines

• Two intersecting lines will form two pairs of vertical angles

• Vertical Angle Theorem: If two angles are vertical angles, then they are congruent

Multiple Choice

Find the value of t

• -1
• 5
• 5.14
• 7

Multiple Choice

Angle 7 and angle 3 are...

• Vertical Angles

• Linear Pairs

• Neither

Poll

Rate your understanding of linear pairs and vertical angles.

• I've got this

• I think I understand, but may have some questions

• I still have lots of questions

• I'm sorry, what were we talking about?

Multiple Choice

Find the value of r

• 46
• 44
• 43
• 47

Multiple Choice

Find the values of y and z.

• y=76, z=114

• y=104, z=76

• y=76, z=104

• z=114, y=76

Multiple Choice

Angle 1 and two are...

• Vertical Angles

• Linear Pairs

• Neither

Multiple Choice

What is the measure of each vertical angle?

• 6 degrees, 6 degrees

• 6 degrees, 174 degrees

• 12 degrees, 12 degrees

• 12 degrees, 168 degrees

Multiple Choice

Find the value of x.

• x=125

• x=55

• x=45

Multiple Choice

Angle 5 and angle 8 are...

• Vertical Angles

• Linear Pairs

• Neither