Using Equations to Solve for Unknown Angles

Student Summary

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 xx in this diagram.

Two lines meet to form 4 angles. An angle is labeled 144 degrees. It's vertical angle is split into 4 smaller angles, x degrees, x degrees, x degrees, 90 degrees.

Using what we know about vertical angles, we can write the equation 3x+90=1443x + 90 = 144 to represent this situation. Then we can solve the equation.

3x+90=1443x+90−90=144−903x=543x⋅13=54⋅13x=18\begin{aligned} 3x + 90 &= 144 \\ 3x + 90 - 90 &= 144 - 90 \\ 3x &= 54 \\ 3x \boldcdot \frac13 &= 54 \boldcdot \frac13 \\ x &= 18 \end{aligned}

Visual / Anchor Chart

Standards

Building On
7.EE.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

Addressing
7.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.

7.EE.4

Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.