try this for yourself!
algebra find the value of x that makes ( m parallel n ).
3.
4.
5.

Question

Accepted Answer

### Problem 3:
# Explanation:
## Step1: Identify angle relationship (vertical & corresponding)
The $120^\circ$ angle and $3x^\circ$ are equal (vertical angles, then corresponding as lines are parallel). So $3x = 120$.
## Step2: Solve for $x$
Divide both sides by 3: $x=\frac{120}{3}=40$.
# Answer: $x = 40$

### Problem 4:
# Explanation:
## Step1: Identify supplementary angles (same - side interior)
For parallel lines, same - side interior angles are supplementary. So $(2x + 15)+135 = 180$.
## Step2: Simplify the equation
$2x+150 = 180$. Subtract 150 from both sides: $2x=180 - 150 = 30$.
## Step3: Solve for $x$
Divide by 2: $x=\frac{30}{2}=15$.
# Answer: $x = 15$

### Problem 5:
# Explanation:
## Step1: Identify supplementary angles (same - side interior or vertical - corresponding)
The $150^\circ$ angle and $(3x - 15)^\circ$ are supplementary (same - side interior angles for parallel lines). So $(3x-15)+150 = 180$ or we can also consider that the angle equal to $(3x - 15)^\circ$ and $150^\circ$ are supplementary.
## Step2: Simplify the equation
$3x+135 = 180$. Subtract 135: $3x=180 - 135 = 45$.
## Step3: Solve for $x$
Divide by 3: $x=\frac{45}{3}=15$? Wait, no, wait. Wait, actually, the angle $(3x - 15)^\circ$ and the angle supplementary to $150^\circ$ (which is $30^\circ$)? Wait, no, let's re - check. Wait, the $150^\circ$ and $(3x - 15)^\circ$ are same - side interior angles? Wait, no, maybe vertical angles. Wait, no, the correct relationship: if $m\parallel n$, then the angle $(3x - 15)^\circ$ and $150^\circ$ are supplementary? Wait, no, let's look at the diagram. The $150^\circ$ and $(3x - 15)^\circ$ should be supplementary (same - side interior angles sum to $180^\circ$). So:
## Step1: Set up the equation
$3x-15 + 150=180$
## Step2: Simplify
$3x + 135=180$
Subtract 135 from both sides: $3x=180 - 135 = 45$
## Step3: Solve for $x$
$x = \frac{45}{3}=15$? Wait, no, that can't be. Wait, maybe the angle $(3x - 15)^\circ$ is equal to the angle supplementary to $150^\circ$. The supplementary angle of $150^\circ$ is $180 - 150=30^\circ$. So $3x-15 = 30$
## Step1 (corrected): Set up the correct equation
$3x-15=30$ (because the angle $(3x - 15)^\circ$ and $150^\circ$ are same - side interior angles, so they are supplementary, so $(3x - 15)=180 - 150 = 30$)
## Step2: Solve for $x$
Add 15 to both sides: $3x=30 + 15=45$
Divide by 3: $x = 15$? Wait, no, $3x-15 = 30$ gives $3x=45$, $x = 15$. Wait, but let's check: $3(15)-15=45 - 15 = 30$, and $30+150 = 180$, which works for supplementary angles. So:
# Explanation:
## Step1: Identify supplementary angles (same - side interior)
$(3x - 15)^\circ$ and $150^\circ$ are supplementary, so $(3x - 15)+150 = 180$ or $(3x - 15)=180 - 150 = 30$.
## Step2: Solve for $x$
From $3x-15 = 30$, add 15: $3x=45$, $x = 15$. Wait, no, that's the same as before. Wait, maybe I made a mistake in the angle relationship. Let's consider that the angle $(3x - 15)^\circ$ and $150^\circ$ are vertical angles? No, the diagram shows a transversal cutting two parallel lines. The $150^\circ$ and $(3x - 15)^\circ$ are same - side interior angles. So their sum is $180^\circ$. So:
$3x-15+150 = 180$
$3x+135 = 180$
$3x=180 - 135 = 45$
$x = 15$. Wait, but when $x = 15$, $3x-15=30$, and $30 + 150=180$, which is correct for supplementary angles. So:
# Answer: $x = 15$ (Wait, no, wait, let's re - check the problem 5 diagram. If the angle is $150^\circ$ and $(3x - 15)^\circ$ are alternate exterior or something? Wait, maybe the angle $(3x - 15)^\circ$ is equal to $150^\circ$'s vertical angle? No, vertical angle of $150^\circ$ is $150^\circ$. Wait, maybe the angle $(3x - 15)^\circ$ and $150^\circ$ are corresponding angles? No, that would mean $3x-15 = 150$, then $3x=165$, $x = 55$. Oh! I see my mistake. If the lines are parallel, and the angle $(3x - 15)^\circ$ and $150^\circ$ are corresponding angles (if the transversal is such that the angle $(3x - 15)^\circ$ and $150^\circ$ are in the same position relative to the parallel lines), then they are equal. So:
## Step1 (corrected): Identify corresponding angles
If $m\parallel n$, then $(3x - 15)^\circ=150^\circ$ (corresponding angles)
## Step2: Solve for $x$
$3x-15 = 150$
Add 15 to both sides: $3x=150 + 15=165$
Divide by 3: $x=\frac{165}{3}=55$
Ah, that makes more sense. I misidentified the angle relationship. So the correct approach is:
# Explanation:
## Step1: Identify corresponding angles (for parallel lines $m\parallel n$)
The angle $(3x - 15)^\circ$ and $150^\circ$ are corresponding angles, so they are equal. Thus, $3x-15 = 150$.
## Step2: Solve for $x$
Add 15 to both sides: $3x=150 + 15 = 165$.
Divide by 3: $x=\frac{165}{3}=55$.
# Answer: $x = 55$

So to summarize:

- Problem 3: $x = 40$
- Problem 4: $x = 15$
- Problem 5: $x = 55$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 3:

Step1: Identify angle relationship (vertical & corresponding)

Step2: Solve for \(x\)

Step1: Identify supplementary angles (same - side interior)

Step2: Simplify the equation

Step3: Solve for \(x\)

Step1: Identify supplementary angles (same - side interior or vertical - corresponding)

Step2: Simplify the equation

Step3: Solve for \(x\)

Step1: Set up the equation

Step2: Simplify

Step3: Solve for \(x\)

Step1 (corrected): Set up the correct equation

Step2: Solve for \(x\)

Answer:

Problem 4: