Transcript Complementary 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.
Quick Check!
1) On your whiteboards, show me what a pair of complementary angles look like and how many degrees they measure.
2) Now, show me on your whiteboards, what a pair of Supplementary angles look like and how many degrees they measure.
Supplementary angles add up to
180º
.
120º 60º
Adjacent and Supplementary Angles
40º 140º
Supplementary Angles but not Adjacent
Complementary angles add up to
90º
.
30º 60º
Adjacent and Complementary Angles
40º 50º
Complementary Angles but not Adjacent
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.
Remember: Two angles are supplementary if the
sum
of their measures is
180 degrees
. Each angle is the
supplement
of the other.
1 20
These are supplements of each other
160
because their angles add up to 180.
2
3 STEPS for Finding Missing Angles:
1) First, create an addition equation by adding both angles.
1) The sum
90
° of the two angles will
for Complementary equal
Angles and
180
°
for Supplementary
Angles.
3) Solve the equation using the inverse rules!
Think…Pair… Share… How are angles part of our outside world? If there were no angles, how do you think our world would be different?
What other subjects can you make connections with that also use Angles?
Example 1 Find the value of x by making an equation.
x
20
x
+ 20
= 180
x
= 160
Example 2 Find the value of x by writing your equation.
x
65
x
+ 65
= 180
x
= 115
Two angles are complementary if the
sum
of their measures is
90 degrees
. Each angle is the
complement
of the other.
30 60
These are complements of each other because their angles add up to be 90.
1 2
Example 3 Find the value of x.
x
x
+ 15
= 90
x
= 75
15
Now, think of what we talked about today.
5 4 1 3 2 Are angles 4 and 5 supplementary angles?
no Are angles 2 and 3 complementary angles?
Are angles 4 and 3 supplementary angles?
no yes Are angles 2 and 1 complementary angles?
yes
Examples FOLDABLE ON ANGLES: Measures less than Measures exactly 90 degrees Measures more than 90 degrees and less than 180 degrees.
90 degrees Measures exactly 180 degrees Vertical Angles
are the angles opposite each other when two lines cross
Two angles that share a same side and same vertex Two angles whose sum is equal to 90 degrees Two angles whose sum is equal to 180 Degrees.
Examples
Example 4 Find the value of x.
(4
x
+ 3) (
x
- 8)
(4
x
5
x
- 5 = 90 5
x
= 95
x
= 19
Example 5 Find the value of x.
(7
x
10) 3
x
(7
x
+ 10) + 3x = 180 10
x
+ 10 = 180
10
x
= 170
x
= 17
Think back to last class…
5 4 1 3 2 Are angles 1 and 2 a linear pair?
Are angles 1 and 3 adjacent angles?
Are angles 3 and 4 a linear pair?
Are angles 2 and 3 adjacent angles?
no no yes yes
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.
Z
Figure 1 find the missing angles you may use a protractor to draw it!
T X
40 50
Q
S R 40
V Y S
A C
Figure 2: find the missing angles you may use a protractor to draw it!
E B
w 20 x y z
G F D
Figure 3
M N P
20 45
X 25
° 45 P- 45 °
Q R L