1. M.G. 2.1 Identify angles as adjacent, vertical,
complementary and supplementary.
Objective-- Students will identify angles as complementary
and supplementary and solve problems with an unknown
angle from given information about them by finding a
missing angle and scoring an 80% proficiency on an exit slip.
2. Warm Up
Identify the type of angle.
1. 70°
2. 90°
3. 140°
4. 180°
acute
right
obtuse
straight
4. Congruent angles have the same measure.
Vertical angles are formed opposite each other
when two lines intersect. Vertical angles have
the same measure, so they are always
congruent.
MRP and NRQ are vertical angles.
MRN and PRQ are vertical angles
5. Adjacent angles are side by side and have a
common vertex and ray. Adjacent angles may or
may not be congruent.
MRN and NRQ are adjacent angles. They
share vertex R and RN.
NRQ and QRP are adjacent angles. They
share vertex R and RQ.
13. Supplementary angles add up to
180º.
60º
120º
40º
140º
Adjacent and Supplementary
Angles
Supplementary Angles
but not Adjacent
14. How can I remember that?
• Draw the S in Supplementary
S
• Since supplementary angles equal 180*, turn that S into a
number 8 by drawing a line diagonal, then add a 1 in front
of that and a 0 after to make it 180.
• So you change the S in supplementary into 180*!!
S S 1S0*
15. Complementary angles add up to
90º.
60º
30º
40º
50º
Adjacent and Complementary
Angles
Complementary Angles
but not Adjacent
16. How can I remember that?
• Draw the C in Complementary
C
• Since complementary angles equal 90*, turn that C into a
number 9 by drawing a line, then add a 0 after that to make
it 90.
• So you change the C in complementary into 90*!!
C C C
17. Remember our Objective…
Students will identify angles as
complementary and
supplementary and solve problems with
an unknown angle from given information about
them by finding a missing angle and scoring an
80% proficiency on an exit slip.
18. Remember: Two angles are supplementary if the sum
of their measures is 180 degrees. Each angle is the
supplement of the other.
1 2
20
160
These are supplements of each other
because their angles add up to 180.
19. 3 STEPS for Finding Missing
Angles:
1) First, create an addition equation by adding both angles.
1) The sum of the two angles will equal
90° for Complementary Angles and
180° for Supplementary Angles.
3) Solve the equation using the inverse rules!
20. x
Example 1 Find the value of x by making
an equation.
x
+ = 180
20
x
= 160
20
21. x
Example 2 Find the value of x by writing
your equation.
65
x
+ = 180
65
x
= 115
22. Two angles are complementary if the sum of their
measures is 90 degrees. Each angle is the
complement of the other.
1
2
30
60
These are complements of each other
because their angles add up to be 90.
23. Example 3 Find the value of x.
x
15
x
+ = 90
15
x = 75
24. 1
2
3
5
Are angles 4 and 5 supplementary angles?
Are angles 2 and 3 complementary angles?
Are angles 2 and 1 complementary angles?
Are angles 4 and 3 supplementary angles?
no
no
yes
yes
Now, think of what we talked about today.
4
25. Example 4 Find the value of x.
(4x + 3)
(x - 8)
(4x + 3) + (x - 8) = 90
x = 19
5x
- 5 = 90
5x
= 95
26. Example 5 Find the value of x.
(7x 10)
3x
(7x + 10) + 3x = 180
10x
+ 10 = 180
10x
= 170
x = 17
27. 1
2
3
5
Are angles 1 and 2 a linear pair?
Are angles 1 and 3 adjacent angles?
Are angles 2 and 3 adjacent angles?
Are angles 3 and 4 a linear pair?
no
no
yes
yes
Think back to last class…
4
28. Remember…Students will identify
angles as complementary
and supplementary and solve
problems with an unknown angle from
given information about them by finding
a missing angle and scoring an 80%
proficiency on an exit slip.
29. Figure 1find the missing angles you may use a
protractor to draw it!
X
Z
Q
S
T
V
Y
40
50
40
R
S
Editor's Notes
#20:This is on p. 16 of the Study Guide problem #2.
#21:This is on p. 16 of the Study Guide problem #3.
#23:This is on p. 16 of the Study Guide problem #1.
#25:This is on p. 16 of the Study Guide problem #6.
#26:This is on p. 16 of the Study Guide problem #3.
#29:This is the 2nd figure in the practice workbook p.16
