You are given two expressions, $3x+16$ and $5x-20$, for a pair of vertical angles. What equation should you write if those two angle measures must be the same?

Once you have your equation, move all the $x$ terms to one side and the constant numbers to the other, then isolate $x$ by undoing multiplication or division.

In Desmos, enter the two equations as functions: y = 3x + 16 and y = 5x - 20. This will graph two straight lines.

Tap or click on the point where the two lines intersect. The x-coordinate of this intersection point is the value of $x$ that makes $3x+16$ and $5x-20$ equal.

When two lines intersect, they form pairs of vertical (opposite) angles. Vertical angles are always congruent, meaning they have the same measure.

You are told one angle measures $(3x+16)^{\circ}$ and the vertical angle measures $(5x-20)^{\circ}$. Because vertical angles are congruent, set their measures equal:

Now solve the equation for $x$.

Subtract $3x$ from both sides:

Add $20$ to both sides:

You now have a simple equation with $x$ on one side.

Divide both sides of $36 = 2x$ by $2$:

Check: if $x=18$, then $3x+16 = 3(18)+16 = 54+16 = 70$ and $5x-20 = 5(18)-20 = 90-20 = 70$, so the two vertical angles are indeed equal. Therefore, the value of $x$ is $18$.