Learning Targets
To find an unknown angle measure, sometimes it is helpful to write and solve an equation that represents the situation. For example, suppose we want to know the value of in this diagram.
Using what we know about vertical angles, we can write the equation 3x + 90 = 144 to represent this situation. Then we can solve the equation.
3x + 90 = 144
3x + 90 - 90 = 144 - 90
3x = 54
divide by 3
x = 18
Elena and Diego each wrote equations to represent these diagrams. For each diagram, decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
Elena: x = 35
Diego: x + 35 = 180
Elena: 35 + w + 41 = 180
Diego: 35 + w = 180
Elena: w + 35 = 90
Diego: 2w + 35 = 90
Elena: 2w + 35 = 90
Diego: w + 35 = 90
Elena: w + 148 = 180
Diego: x + 90 = 148
Find the unknown angle measures. Show your thinking. Organize it so it can be followed by others.
1.
2.
3. Lines l and m are perpendicular.
4.
How can equations help us solve for an unknown angle measure?
Is there only one way to solve for an unknown angle measure?