complementary angles and supplementary angles
DESCRIPTION
Complementary Angles and Supplementary Angles. M.G. 2.1 Identify angles as adjacent, vertical, complementary and supplementary. - PowerPoint PPT PresentationTRANSCRIPT
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.
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
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 2
20160
These are supplements of each other because their angles add up to 180.
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!
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 useAngles?
x
Example 1 Find the value of x by making an equation.
x + = 18020
x = 160
20
x
Example 2 Find the value of x by writing your equation.
65
x + = 18065
x = 115
Two angles are complementary if the sum of their measures is 90 degrees. Each angle is the complement of the other.
12
3060
These are complements of each other because their angles add up to be 90.
Example 3 Find the value of x.
x
15x + = 9015
x = 75
12
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
Vertical Angles are the angles opposite each other when two lines cross
FOLDABLE ON ANGLES:
Measures less than
90 degrees
Measures exactly
90 degrees
Measures more than 90 degrees and less than 180 degrees.
Measures exactly
180 degrees
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
Examples
Examples
Examples
Examples
Examples
Examples
Example 4 Find the value of x.
(4x + 3)
(x - 8)
(4x + 3) + (x - 8) = 90
x = 19
5x - 5 = 905x = 95
Example 5 Find the value of x.
(7x 10) 3x
(7x + 10) + 3x = 180 10x + 10 = 180
10x = 170
x = 17
12
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
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.
Figure 1find the missing angles you may use a protractor to draw
it!
X
Z
Q
S
T
V
Y
4050
40R
S
Figure 2: find the missing angles you
may use a protractor to draw it!
A
CF D
B
E
G
20 xy
zw
Figure 3
N
M
X - 25°
L
P
Q
R4545
20
P- 45°