Question

if line l is parallel to line m, find the values of x and y.
x =
y =

Explanation:

Step1: Use the property of corresponding angles

Since line $l$ is parallel to line $m$, the corresponding - angles are equal. The angle $(2x + 13)^{\circ}$ and the angle $(3x)^{\circ}$ are corresponding angles. So we set up the equation $2x+13 = 3x$.
$2x+13=3x$
$3x - 2x=13$
$x = 13$

Step2: Use the property of alternate - interior angles

The angle $(5y - 23)^{\circ}$ and the $47^{\circ}$ angle are alternate - interior angles. Since line $l$ is parallel to line $m$, alternate - interior angles are equal. So we set up the equation $5y-23 = 47$.
$5y=47 + 23$
$5y=70$
$y=\frac{70}{5}=14$

Answer:

$x = 13$
$y = 14$