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? (4x + 7)° (6x - 63)° the angles are select, so they are select consecutive interior alternate exterior corresponding alternate interior consecutive exterior

Explanation:

Step1: Identify angle - type

The angles $(4x + 7)^{\circ}$ and $(6x - 63)^{\circ}$ are alternate interior angles since they are between the two parallel lines $l$ and $m$ and on opposite sides of the transversal.

Step2: Use angle - property

For parallel lines, alternate interior angles are congruent. So, we set up the equation $4x+7 = 6x - 63$.

Step3: Solve the equation

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, so they are congruent. $x = 35$