adjacent, vertical, complementary and supplementary angles

ADJACENT, VERTI

CAL,

COMPLEMENTARY

AND

SUPPLEMENTARY

ANGLES

M R . PE T E R S O N

CC STANDARD 7.G.5USE FACTS ABOUT SUPPLEMENTARY, COMPLEMENTARY, VERTICAL, AND ADJACENT ANGLES IN A MULTI-STEP PROBLEM TO WRITE AND SOLVE SIMPLES EQUATIONS FOR AN UNKNOWN ANGLE IN A FIGURE.

Paraphrase:• Identify adjacent and vertical angels.• Find angel measures using adjacent and vertical

angles.• Classify pairs of angles as complementary,

supplementary, or neither.• Find angle measures using complementary and

supplementary angles.

INPUT Vertex - Endpoint where two line segments or lines come

together. Adjacent angles – Angles that share a common side and

have the same vertex. Vertical angles – Opposite angles formed by the

intersection of two lines. Congruent angles – Angles that have the same measure. Complementary angles – Two angles whose sum of their

measure is 90°. Supplementary angles - Two angles whose sum of their

measure is 180°.

Anglesthat measure less than 90°.

Angles that measure more than 90°and less than 180°.

Anglesthat measure exactly 90°.

Types of Angles

Acute -

Right - Anglesthat measure exactly 180°.

Obtuse -

Straight -

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 (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

GUIDED PRACTICEDIRECTIONS: 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

PROTRACTOR WORK: GUIDED PRACTICE

1. Draw a straight line.

170 10

160 20

150 30

140 40

130 50

120 60110 70

100 8090 80

100 70110 60

120 5013

0

40

140

30

150

20

160

10

170

PROTRACTOR WORK: GUIDED PRACTICE

2. Draw a ray to form an angle of 40°from the right side.

170 10

160 20

150 30

140 40

130 50

120 60110 70

100 8090 80

100 70110 60

120 5013

0

40

140

30

150

20

160

10

170

PROTRACTOR WORK: GUIDED PRACTICE

3. Find the measure of the angle supplementary to the angle you just created.

40°140°

PROTRACTOR WORK: GUIDED PRACTICE

4. Use a straightedge to extend the ray you drew to below the line.

40°140°

PROTRACTOR WORK: GUIDED PRACTICE

5. What is the measure of angle X?

40°140°

40° x y 140°

Angle Y?

How did you find the answer?

Why?

TIME FOR YOU TO TRY SOME ON YOUR OWN