1. Complementary Angles and Supplementary Angles
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

3. Vocabulary congruent vertical angles adjacent angles
complementary angles
supplementary angles

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 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.

6. Adjacent angles are “side by side” and share a common ray.
15º
45º

7. These are examples of adjacent angles.
45º
80º
35º
55º
130º
50º
85º
20º

8. These angles are NOT adjacent.
100º
50º
35º
35º
55º
45º

9. When 2 lines intersect, they make vertical angles.
75º
105º
105º
75º

10. Vertical angles are opposite one another.
75º
105º
105º
75º

11. Vertical angles are opposite one another.
75º
105º
105º
75º

12. Vertical angles are congruent (equal).
150º
30º
150º
30º

13. Supplementary angles add up to 180º.
40º
120º
60º
140º
Adjacent and Supplementary Angles
Supplementary Angles but not Adjacent

14. S S S 1S0* How can I remember that? Draw the S in Supplementary
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.
30º
40º
50º
60º
Adjacent and Complementary Angles
Complementary Angles but not Adjacent

16. C C C C How can I remember that? Draw the C in Complementary
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. Supplementary Angles
Remember: Two angles are supplementary if the sum of their measures is 180 degrees. Each angle is the supplement of the other. 1 2
These are supplements of each other because their angles add up to 180.

19. 3 STEPS for Finding Missing Angles:
First, create an addition equation by adding both angles.
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. Example 1 Find the value of x by making an equation.
This is on p. 16 of the Study Guide problem #2.

21. Example 2 Find the value of x by writing your equation.
This is on p. 16 of the Study Guide problem #3.

22. Complementary Angles
Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other. 1 2
These are complements of each other because their angles add up to be 90.

23. Example 3 Find the value of x.
This is on p. 16 of the Study Guide problem #1.

24. 1 5 2 4 3 Now, think of what we talked about today. no
Are angles 4 and 5 supplementary angles? no
Are angles 2 and 3 complementary angles?
Are angles 4 and 3 supplementary angles?
yes
Are angles 2 and 1 complementary angles?
yes

25. Example 4 Find the value of x.
This is on p. 16 of the Study Guide problem #6.

26. Example 5 Find the value of x.
This is on p. 16 of the Study Guide problem #3.

27. 1 5 2 4 3 Think back to last class… no
Are angles 1 and 2 a linear pair? no
Are angles 1 and 3 adjacent angles?
yes
Are angles 3 and 4 a linear pair?
Are angles 2 and 3 adjacent angles?
yes

28. Let's practice. Exit Slip!
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 Q R V S Z Y
This is the 2nd figure in the practice workbook p.16 S