Adjacent, Linear Pairs

Vertical, Supplementary, and

Complementary Angles

Objectives-What we’ll learn…

• Identify and use adjacent angles and linear pairs of angles.

• Identify and use vertical, complementary and 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

Linear pair of angles• two angles that share a

vertex form a straight line (add to 180°)

AEB & BED are a linear pair of angles. They form a straight line & 50+130=180.

When 2 lines intersect, they make vertical angles.

75º

75º

105º105º

Vertical angles are opposite to one another.

75º

75º

105º105º

Vertical angles are opposite one another.

75º

75º

105º105º

Vertical angles are congruent (equal).

30º150º

150º30º

Supplementary angles add up to 180º.

60º120º

40º

140º

Adjacent and Supplementary Angles

Supplementary Anglesbut not Adjacent

Complementary angles add up to 90º.

60º

30º40º

50º

Adjacent and Complementary Angles

Complementary Anglesbut not Adjacent

Practice Time!

Directions: Identify each pair of angles as

vertical, supplementary, complementary,

or none of the above.

#1

60º120º

#1

60º120º

Supplementary Angles

#2

60º30º

#2

60º30º

Complementary Angles

#3

75º75º

#3

75º75º

Vertical Angles

#4

60º40º

#4

60º40º

None of the above

#5

60º

60º

#5

60º

60º

Vertical Angles

#6

45º135º

#6

45º135º

Supplementary Angles

#7

65º

25º

#7

65º

25º

Complementary Angles

#8

50º90º

#8

50º90º

None of the above

Directions:Determine the missing angle.

#1

45º?º

#1

45º135º

#2

65º

?º

#2

65º

25º

#3

35º

?º

#3

35º

35º

#4

50º

?º

#4

50º

130º

#5

140º

?º

#5

140º

140º

#6

40º

?º

#6

40º

50º

Applications of Complementary and

Supplementary Angles

Let x = the measure of an angle, then = complement of the angle, and = supplement of the angle

90o x180o x

Now let us apply this information.

Example #1

The measure of an angle is 4 times the measure of its complement. Find the measure of the angle and the measure of its complement.

Solution (Method #1)Let x = the measure of the complement.Let 4x = the measure of the angle

x + 4x = 905x = 90

x = 18 (measure of the complement)4x = 72 (measure of the angle)

Example #1

Method #2

Let x = the measure of the angleLet 90 – x – measure of the complement

x = 4(90 – x)x = 360 - 4x5x = 360x = 72 (angle measure)90 – x = 18 (complement measure)

Example #2

The ratio of the complement of an angle to the supplement of the angle is 2:7. Find the measure of the original angle.

Solution:Let x = the angle measureLet 90 – x = measure of the complementLet 180 – x = measure of the supplement

90 2

180 7

x

x

Example #2 (Continued)

7(90 ) 2(180 )

630 7 360 2

270 5

54

x x

x x

x

x

90 2

180 7

x

x