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ADJACENT, VERTI
CAL,
COMPLEMENTARY
AND
SUPPLEMENTARY
ANGLES
M R . PE T E R S O N
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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.
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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°.
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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 -
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ADJACENT ANGLES ARE “SIDE BY SIDE” AND SHARE A COMMON RAY.
45º15º
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THESE ARE EXAMPLES OF ADJACENT ANGLES.
55º
35º
50º130º
80º 45º
85º20º
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THESE ANGLES ARE NOT ADJACENT.
45º55º
50º100º
35º
35º
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WHEN 2 LINES INTERSECT, THEY MAKE VERTICAL ANGLES.
75º
75º
105º105º
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Vertical angles are opposite one another.
75º
75º
105º105º
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Vertical angles are opposite one another.
75º
75º
105º105º
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Vertical angles are congruent (equal).
30º150º
150º30º
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SUPPLEMENTARY ANGLES ADD UP TO 180º.
60º120º
40º
140º
Adjacent and Supplementary Angles
Supplementary Anglesbut not Adjacent
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COMPLEMENTARY ANGLES ADD UP TO 90º.
60º
30º40º
50º
Adjacent and Complementary Angles
Complementary Anglesbut not Adjacent
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GUIDED PRACTICEDIRECTIONS: IDENTIFY EACH PAIR OF ANGLES AS VERTICAL, SUPPLEMENTARY, COMPLEMENTARY, OR NONE OF THE ABOVE.
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#1
60º120º
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#1
60º120º
Supplementary Angles
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#2
60º30º
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#2
60º30º
Complementary Angles
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#3
75º75º
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#3
75º75º
Vertical Angles
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#4
60º40º
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#4
60º40º
None of the above
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#5
60º
60º
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#5
60º
60º
Vertical Angles
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#6
45º135º
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#6
45º135º
Supplementary Angles
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#7
65º
25º
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#7
65º
25º
Complementary Angles
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#8
50º90º
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#8
50º90º
None of the above
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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
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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
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PROTRACTOR WORK: GUIDED PRACTICE
3. Find the measure of the angle supplementary to the angle you just created.
40°140°
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PROTRACTOR WORK: GUIDED PRACTICE
4. Use a straightedge to extend the ray you drew to below the line.
40°140°
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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?
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TIME FOR YOU TO TRY SOME ON YOUR OWN