Question

find the values of x and y.
(12x)°
42°
(6y)°
x =
y =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. The angle with measure $(12x)^{\circ}$ and the angle with measure $42^{\circ}$ are vertical angles. So, $12x = 42$.

Step2: Solve for x

Divide both sides of the equation $12x = 42$ by 12. $x=\frac{42}{12}=\frac{7}{2}=3.5$.

Step3: Use right - angle property

The angle with measure $(6y)^{\circ}$ and the right - angle together form a straight - line, and the measure of a straight - line angle is $180^{\circ}$. So, $6y+90 = 180$.

Step4: Solve for y

Subtract 90 from both sides of the equation $6y + 90=180$: $6y=180 - 90=90$. Then divide both sides by 6. $y=\frac{90}{6}=15$.

Answer:

$x = 3.5$
$y = 15$