ObjectivesAngle Pair Relationships

◦Adjacent Angles◦Vertical Angles◦Linear Pair◦Complementary Angles◦Supplementary Angles

Adjacent angles are “side by side” and share a common ray.

45º15º

These are examples of adjacent angles.

55º

35º

50º130º

80º 45º

85º20º

These angles are NOT adjacent.

45º55º

50º100º

35º

35º

When 2 lines intersect, they make vertical angles.

75º

75º

105º105º

Vertical angles are opposite one another.

75º

75º

105º105º

Vertical angles are opposite one another.

75º

75º

105º105º

Vertical angles are congruent

30º150º

150º30º

Supplementary angles add up to 180º.

60º120º

40º

140º

Adjacent and Supplementary

Angles

Supplementary Angles

but not Adjacent

Complementary angles add up to 90º.

60º

30º40º

50º

Adjacent and Complementary

Angles

Complementary Angles

but not Adjacent

Linear Pair

Two adjacent angles (common vertex and a common ray) that form a straight line. So the two angles add up to ?180

Practice Time!

Directions:

Identify each pair of angles as vertical, supplementary, complementary, linear pairor none of the above.

#1

60º120º

Supplementary Angles

And a Linear Pair

#2

60º30º

Complementary Angles

#3

75º75º

Vertical Angles

#4

60º40º

None of the above

#5

60º

60º

Vertical Angles

#6

45º135º

Supplementary Angles and a Linear Pair

#7

65º

25º

Complementary Angles

#8

50º90º

None of the above

Directions:

Determine the missing angle.

#1

45º?

#1

45º135º

#2

65º

#2

65º

25º

#3

35º

#3

35º

35º

#4

50º

?

#4

50º

130º

#5

140º

?

#5

140º

140º

#6 Rectangle

40º

?

#6 Rectangle

40º50º

SOLUTION

EXAMPLE Find angle measures in a linear pair

Let x° be the measure of one angle. The measure of the other angle is 5x°. Then use the fact that the angles of a linear pair are supplementary to write an equation.

Two angles form a linear pair. The measure of one angle is 5 times the measure of the other. Find the measure of each angle.

ALGEBRA

EXAMPLE Find angle measures in a linear pair

x + 5x = 180°6x = 180°x = 30°

Write an equation.

Combine like terms.

Divide each side by 6.

The measures of the angles are 30° and 5(30)° = 150°.

ANSWER

Find m< AEB

4x +8

6x - 42

Write an equation & Solve 

Find the measure of each <

Write an equation & Solve 

Homework

Page 38 # 3 – 42 (x3) and 49 – 52 all

Honors also: # 45, 55, & 56