Question

the given lines are parallel. provide the value of x and the measure of the angles. (13x - 21) (5x + 75)

Explanation:

Step1: Use property of parallel lines

When two parallel lines are cut by a transversal, corresponding - angles (or alternate - interior/alternate - exterior angles in appropriate cases) are equal. Here, we assume the two given angles are equal. So we set up the equation $13x - 21=5x + 75$.

Step2: Solve the equation for x

Subtract $5x$ from both sides:
$13x-5x - 21=5x-5x + 75$
$8x-21 = 75$.
Then add 21 to both sides:
$8x-21 + 21=75 + 21$
$8x=96$.
Divide both sides by 8:
$x=\frac{96}{8}=12$.

Step3: Find the measure of the angles

Substitute $x = 12$ into either of the angle expressions. Let's use $5x + 75$.
$5\times12+75=60 + 75=135$.

Answer:

$x = 12$, measure of the angles is $135^{\circ}$