Question

find the value of $x$ that makes $m \parallel n$. explain your reasoning. (see example 1.)
4)
5)
8)

Explanation:

Step1: Problem 4: Identify supplementary angles

When $m \parallel n$, same-side interior angles are supplementary, so:
$$(2x + 15) + 135 = 180$$

Step2: Problem 4: Simplify and solve for $x$

$$2x + 150 = 180$$
$$2x = 30$$
$$x = 15$$

Step3: Problem 5: Identify congruent angles

When $m \parallel n$, alternate interior angles are congruent, so:
$$3x - 15 = 150$$

Step4: Problem 5: Simplify and solve for $x$

$$3x = 165$$
$$x = 55$$

Step5: Problem 8: Identify congruent angles

When $m \parallel n$, corresponding angles are congruent, so:
$$3x = 2x + 20$$

Step6: Problem 8: Solve for $x$

$$3x - 2x = 20$$
$$x = 20$$

Answer:

1. For problem 4: $x = 15$
2. For problem 5: $x = 55$
3. For problem 8: $x = 20$