Math / Geometry

QuestionFind the value of $x$ that makes $m \| n$ .
DOL:

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes lines $m$ and $n$ parallel, given two angles formed by a line crossing them. Watch out! Remember, there are multiple angle relationships when lines are crossed by another line, so make sure you pick the right one!

STEP 2

1. Set up the equation
2. Solve for $x$

STEP 3

Hey everyone!
Notice that the angles measuring $3x^\circ$ and $(x + 20)^\circ$ are corresponding angles.
If lines $m$ and $n$ are parallel, corresponding angles are equal!

STEP 4

So, we can set up the equation: $3x = x + 20$ This equation says that if the angles are equal, then the lines are parallel.

STEP 5

Let's isolate $x$ by subtracting $x$ from both sides of the equation.
Remember, what we do on one side, we must do to the other! $3x - x = x + 20 - x$ $2x = 20$ We subtracted $x$ to move all the $x$ terms to one side, making it easier to solve!

STEP 6

Now, let's divide both sides by $2$ to get $x$ all by itself: $\frac{2x}{2} = \frac{20}{2}$ $x = 10$ We divide by $\bf{2}$ because $\bf{2}$ multiplied by $x$ is $2x$ , and we want to find the value of just one $x$ .
Dividing by $2$ gets us there!

STEP 7

Therefore, the value of $x$ that makes $m \parallel n$ is $\bf{10}$ .

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QuestionFind the value of $x$ that makes $m \| n$ .
DOL:

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes lines $m$ and $n$ parallel, given two angles formed by a line crossing them. Watch out! Remember, there are multiple angle relationships when lines are crossed by another line, so make sure you pick the right one!

STEP 2

1. Set up the equation
2. Solve for $x$

STEP 3

Hey everyone!
Notice that the angles measuring $3x^\circ$ and $(x + 20)^\circ$ are corresponding angles.
If lines $m$ and $n$ are parallel, corresponding angles are equal!

STEP 4

So, we can set up the equation: $3x = x + 20$ This equation says that if the angles are equal, then the lines are parallel.

STEP 5

Let's isolate $x$ by subtracting $x$ from both sides of the equation.
Remember, what we do on one side, we must do to the other! $3x - x = x + 20 - x$ $2x = 20$ We subtracted $x$ to move all the $x$ terms to one side, making it easier to solve!

STEP 6

Now, let's divide both sides by $2$ to get $x$ all by itself: $\frac{2x}{2} = \frac{20}{2}$ $x = 10$ We divide by $\bf{2}$ because $\bf{2}$ multiplied by $x$ is $2x$ , and we want to find the value of just one $x$ .
Dividing by $2$ gets us there!

STEP 7

Therefore, the value of $x$ that makes $m \parallel n$ is $\bf{10}$ .

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QuestionFind the value of xxx that makes m∥nm \| nm∥n.DOL:

Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx that makes lines mmm and nnn parallel, given two angles formed by a line crossing them. Watch out! Remember, there are *multiple* angle relationships when lines are crossed by another line, so make sure you pick the right one!

STEP 2

1. Set up the equation2. Solve for xxx

STEP 3

Hey everyone!Notice that the angles measuring 3x∘3x^\circ3x∘ and (x+20)∘(x + 20)^\circ(x+20)∘ are *corresponding angles*.If lines mmm and nnn are parallel, corresponding angles are *equal*!

STEP 4

So, we can **set up** the equation: 3x=x+203x = x + 203x=x+20 This equation says that if the angles are equal, then the lines are parallel.

STEP 5

Let's **isolate** xxx by subtracting xxx from both sides of the equation.Remember, what we do on one side, we *must* do to the other! 3x−x=x+20−x3x - x = x + 20 - x3x−x=x+20−x 2x=202x = 202x=20We subtracted xxx to move all the xxx terms to one side, making it easier to solve!

STEP 6

Now, let's **divide** both sides by 222 to get xxx all by itself: 2x2=202 \frac{2x}{2} = \frac{20}{2} 22x​=220​ x=10 x = 10 x=10We divide by 2\bf{2}2 because 2\bf{2}2 multiplied by xxx is 2x2x2x, and we want to find the value of just one xxx.Dividing by 222 gets us there!

STEP 7

Therefore, the value of xxx that makes m∥nm \parallel nm∥n is 10\bf{10}10.

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QuestionFind the value of $x$ that makes $m \| n$ .
DOL:

What is this asking? We need to find the value of $x$ that makes lines $m$ and $n$ parallel, given two angles formed by a line crossing them. Watch out! Remember, there are multiple angle relationships when lines are crossed by another line, so make sure you pick the right one!

1. Set up the equation
2. Solve for $x$

Hey everyone!
Notice that the angles measuring $3x^\circ$ and $(x + 20)^\circ$ are corresponding angles.
If lines $m$ and $n$ are parallel, corresponding angles are equal!

So, we can set up the equation: $3x = x + 20$ This equation says that if the angles are equal, then the lines are parallel.

Let's isolate $x$ by subtracting $x$ from both sides of the equation.
Remember, what we do on one side, we must do to the other! $3x - x = x + 20 - x$ $2x = 20$ We subtracted $x$ to move all the $x$ terms to one side, making it easier to solve!

Now, let's divide both sides by $2$ to get $x$ all by itself: $\frac{2x}{2} = \frac{20}{2}$ $x = 10$ We divide by $\bf{2}$ because $\bf{2}$ multiplied by $x$ is $2x$ , and we want to find the value of just one $x$ .
Dividing by $2$ gets us there!

Therefore, the value of $x$ that makes $m \parallel n$ is $\bf{10}$ .