Question

lines l and m are parallel. what kind of angles are shown in the figure? what does this tell us about their measures? what is the value of x? the angles are select, so they are select. x = select

Explanation:

Step1: Identify angle - type

The angles $(4x + 7)^{\circ}$ and $(6x-63)^{\circ}$ are alternate - interior angles since lines $l$ and $m$ are parallel. Alternate - interior angles are congruent.

Step2: Set up the equation

Since the alternate - interior angles are equal, we set up the equation $4x + 7=6x - 63$.

Step3: Solve the equation for $x$

First, subtract $4x$ from both sides:
$4x+7-4x=6x - 63-4x$
$7 = 2x-63$.
Then add 63 to both sides:
$7 + 63=2x-63 + 63$
$70 = 2x$.
Finally, divide both sides by 2:
$\frac{70}{2}=\frac{2x}{2}$
$x = 35$.

Answer:

The angles are alternate - interior angles, so they are congruent. $x = 35$