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

7.EE.B.4

Addressing
7.G.5

7.G.B.5

7.EE.4

7.EE.B.4

7.G.5

7.G.B.5

7.EE.4

7.EE.B.4

7.G.5

7.G.B.5