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.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles. So, $4x = 72$.

Step2: Solve for $x$

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

Step3: Use linear - pair property

$\angle2$ and $\angle3$ form a linear - pair. The sum of angles in a linear - pair is $180^{\circ}$. So, $y + 72=180$.

Step4: Solve for $y$

Subtract 72 from both sides of the equation $y + 72 = 180$. We get $y=180 - 72=108$.

Answer:

$x = 18$
$y = 108$