ADJACENT,
VERT
ICAL,
COMPLEMENTA
RY AND
SUPPLE
MENTARY
ANGLES
MR
. P
ET
ER
SO
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 60
110 70
100 80
90 80100 70
110 60120
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 60
110 70
100 80
90 80100 70
110 60120
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
