Question

in the figure below, the measure of ∠1 = 4x°, the measure of ∠2 = y°, and the measure of ∠3 = 72°. find the value of each variable. (type a whole number.) x = □

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles. So, $4x=y$ and $\angle1=\angle3$. Since $\angle3 = 72^{\circ}$, then $4x=72$.

Step2: Solve for $x$

Divide both sides of the equation $4x = 72$ by 4. We get $x=\frac{72}{4}=18$.

Step3: Find the measure of $\angle2$

$\angle2$ and $\angle3$ are supplementary (linear - pair of angles, sum to $180^{\circ}$). So, $\angle2=180 - \angle3$. Substitute $\angle3 = 72^{\circ}$, then $\angle2=180 - 72=108^{\circ}$, and $y = 108$.

Answer:

$x = 18$