Question

in the figure below, the measure of ∠1 = 5x°, the measure of ∠2 = y°, and the measure of ∠3 = 80°. find the value of each variable.
x = 16 (type a whole number.)
y = (type a whole number.)

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle1$ and $\angle3$ are vertical angles, so $5x = 80$.

Step2: Solve for $x$

Divide both sides of the equation $5x = 80$ by 5. We get $x=\frac{80}{5}=16$.

Step3: Use adjacent - angle property

$\angle1$ and $\angle2$ are adjacent angles on a straight - line, so $\angle1+\angle2 = 180^{\circ}$ (linear pair). Since $\angle1 = 80^{\circ}$, then $y=180 - 80=100$.

Answer:

$x = 16$, $y = 100$