Question

in the figure below, the measure of ∠1 = 3x°, 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 $\angle1=\angle3$.
Since $\angle1 = 3x$ and $\angle3=72^{\circ}$, we have the equation $3x = 72$.

Step2: Solve the equation for $x$

Divide both sides of the equation $3x = 72$ by 3. We get $x=\frac{72}{3}=24$.

Step3: Find the measure of $\angle2$

$\angle2$ and $\angle3$ are supplementary angles (they form a linear - pair), so $\angle2+\angle3 = 180^{\circ}$. Since $\angle3 = 72^{\circ}$, then $\angle2=180 - 72=108^{\circ}$, and $y = 108$.

Answer:

$x = 24$