Question

in exercises 2, 3, 4 find the value of x that makes m || n. explain your
2.
statements
reasons
(2x + 15)°
3.
statements
reasons
(13x - 15)°
4.
statements
reasons
(180 - x)°

Explanation:

Step1: Identify corresponding - angles property

When $m\parallel n$, corresponding angles are equal. In the first - type of problem (the first diagram), if we assume the two angles are corresponding angles, we set up the equation $2x + 15=135$.

Step2: Solve the equation for $x$

Subtract 15 from both sides of the equation $2x + 15=135$:
$2x=135 - 15$
$2x = 120$
Divide both sides by 2: $x=\frac{120}{2}=60$.

In the second - type of problem (the second diagram), if we assume the two angles are corresponding angles, we set up the equation $3x-15 = 135$.

Step3: Solve the new equation for $x$

Add 15 to both sides: $3x=135 + 15$
$3x=150$
Divide both sides by 3: $x = 50$.

In the third - type of problem (the third diagram), if the two angles are alternate interior angles (since $m\parallel n$), we set up the equation $180 - x=x$.

Step4: Solve the equation for $x$

Add $x$ to both sides: $180=2x$
Divide both sides by 2: $x = 90$.

Answer:

For the first problem: $x = 60$
For the second problem: $x = 50$
For the third problem: $x = 90$