Question

in the figure below, k || l. find the values of x and y.

Explanation:

Step1: Use property of supplementary angles

Since $x$ and the $78^{\circ}$ - angle are supplementary (linear - pair of angles), we have $x + 78=180$.
$x=180 - 78$

Step2: Solve for $x$

$x = 102$

Step3: Use property of corresponding angles

The $(4y - 54)^{\circ}$ - angle and the $78^{\circ}$ - angle are corresponding angles. Since $k\parallel l$, we set up the equation $4y-54 = 78$.

Step4: Solve for $y$

First, add 54 to both sides of the equation: $4y=78 + 54$, so $4y=132$. Then divide both sides by 4: $y=\frac{132}{4}=33$.

Answer:

$x = 102$
$y = 33$