1. Seventh Grade Geometry Unit 5

2. Warm Up
Write an equation to solve for x. The angle is a right angle.
Then find the two angle measurements.
6x + 3x = 90
9x = 90
x = 10
Plug 10 back in for each x to find the two angles.
6(10) = 60º
3(10) = 30º
6xº
3xº

3. MCC7.G.5. Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

4. Essential Questions
How can I use the special angle relationships – supplementary, complementary, vertical, and adjacent – to write and solve equations for multi-step problems?

5. Solve for x and then find the angle measurements.
7x + x + 20 = 180
8x + 20 = 180
x = 20
7(20) = 140º
(20) = 40º

6. Solve for x and then find the angle measurements.
2x = 5x – 108
108 = 3x
36 = x
2(36) = 72º
5(36) – 108 = 72º

7. If one angle in a pair of vertical angles measures 70° and the other measures (3n – 8) , what is the value of n?
3n – 8 = 70
n = 26

8. One of two complementary angles has a measure that is 4 times that of the other angle. Which could be used to find n, the degree measure of the smallest angle?
a. 4n = 90
b. n + 4n = 90
c. 4n = 180
d. n + 4n = 180

9. The measure of angle 2 is two times larger than measure of angle 1.3 4
Classify the following pairs of angles.
Use each of the following terms only once: supplementary, adjacent, and vertical.
Angle 1 and angle 2 ________________
Angle 1 and angle 3 ________________
Angle 2 and angle 3 ________________
Find the measures of all 4 angles.
Supplementary or Adjacent
Vertical
Adjacent or Supplementary
n + 2n = 180
m<1 = 60°
m<2 = 120°
m<3 = 60°
m<4 = 120°

10. Closing
Write an equation to solve for x and then find the algebraic angle.
9x – 4 = 140
x = 16
9x – 4
9(16) – 4
140º