Question

in the figure below, the measure of $angle1 = 4x^{circ}$, the measure of $angle2 = y^{circ}$, and the measure of $angle3 = 80^{circ}$. find the value of each variable.

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles.
So, $4x = 80$.

Step2: Solve for $x$

Divide both sides of the equation $4x = 80$ by 4.
$x=\frac{80}{4}=20$.

Step3: Identify supplementary - angle relationship

$\angle2$ and $\angle3$ are supplementary angles (they form a straight - line), so $\angle2+\angle3 = 180^{\circ}$.
$y + 80=180$.

Step4: Solve for $y$

Subtract 80 from both sides of the equation $y + 80=180$.
$y=180 - 80=100$.

Answer:

$x = 20$, $y = 100$