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.

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

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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…

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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°