Math / Geometry

QuestionScore: $4 / 5$ Penalty: 1 off
Question Show Examples $\angle 1$ and $\angle 2$ are vertical angles. If $\mathrm{m} \angle 1=(4 x+13)^{\circ}$ and $\mathrm{m} \angle 2=(7 x+4)^{\circ}$ , then find the value of $x$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the measures of two vertical angles equal. Watch out! Don't forget that vertical angles are always equal, so set their expressions equal to each other!

STEP 2

1. Set the expressions equal
2. Solve for $x$

STEP 3

Alright, let's start by remembering that vertical angles are equal!
So, we can set the expressions for the angles equal to each other.
We have:
$(4x + 13)^\circ = (7x + 4)^\circ$
This equation is our starting point to find $x$ .

STEP 4

First, let's subtract $4x$ from both sides to get all the $x$ terms on one side.
This gives us:
$13 = 3x + 4$
Why did we do this?
To isolate the $x$ terms and make it easier to solve for $x$ !

STEP 5

Next, subtract 4 from both sides to get:
$9 = 3x$
Now, we have a simpler equation!
We're getting closer!

STEP 6

Finally, divide both sides by 3 to solve for $x$ :
$x = 3$
And there we have it!
We found the value of $x$ .

STEP 7

The value of $x$ that makes the measures of the vertical angles equal is $x = 3$ .

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QuestionScore: $4 / 5$ Penalty: 1 off
Question Show Examples $\angle 1$ and $\angle 2$ are vertical angles. If $\mathrm{m} \angle 1=(4 x+13)^{\circ}$ and $\mathrm{m} \angle 2=(7 x+4)^{\circ}$ , then find the value of $x$ .
Answer Attempt 1 out of 2 $\square$ Submit Answer

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ that makes the measures of two vertical angles equal. Watch out! Don't forget that vertical angles are always equal, so set their expressions equal to each other!

STEP 2

1. Set the expressions equal
2. Solve for $x$

STEP 3

Alright, let's start by remembering that vertical angles are equal!
So, we can set the expressions for the angles equal to each other.
We have:
$(4x + 13)^\circ = (7x + 4)^\circ$
This equation is our starting point to find $x$ .

STEP 4

First, let's subtract $4x$ from both sides to get all the $x$ terms on one side.
This gives us:
$13 = 3x + 4$
Why did we do this?
To isolate the $x$ terms and make it easier to solve for $x$ !

STEP 5

Next, subtract 4 from both sides to get:
$9 = 3x$
Now, we have a simpler equation!
We're getting closer!

STEP 6

Finally, divide both sides by 3 to solve for $x$ :
$x = 3$
And there we have it!
We found the value of $x$ .

STEP 7

The value of $x$ that makes the measures of the vertical angles equal is $x = 3$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the value of x x x that makes the measures of two vertical angles equal. Watch out! Don't forget that vertical angles are always equal, so set their expressions equal to each other!

STEP 2

1. Set the expressions equal2. Solve for x x x

STEP 3

Alright, let's start by remembering that vertical angles are equal!So, we can set the expressions for the angles equal to each other.We have:(4x+13)∘=(7x+4)∘(4x + 13)^\circ = (7x + 4)^\circ(4x+13)∘=(7x+4)∘This equation is our starting point to find x x x.

STEP 4

First, let's **subtract 4x 4x 4x from both sides** to get all the x x x terms on one side.This gives us:13=3x+413 = 3x + 413=3x+4Why did we do this?To isolate the x x x terms and make it easier to solve for x x x!

STEP 5

Next, **subtract 4 from both sides** to get:9=3x9 = 3x9=3xNow, we have a simpler equation!We're getting closer!

STEP 6

Finally, **divide both sides by 3** to solve for x x x:x=3x = 3x=3And there we have it!We found the value of x x x.

STEP 7

The value of x x x that makes the measures of the vertical angles equal is x=3 x = 3 x=3.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? We need to find the value of $x$ that makes the measures of two vertical angles equal. Watch out! Don't forget that vertical angles are always equal, so set their expressions equal to each other!

1. Set the expressions equal
2. Solve for $x$

Alright, let's start by remembering that vertical angles are equal!
So, we can set the expressions for the angles equal to each other.
We have:
$(4x + 13)^\circ = (7x + 4)^\circ$
This equation is our starting point to find $x$ .

First, let's subtract $4x$ from both sides to get all the $x$ terms on one side.
This gives us:
$13 = 3x + 4$
Why did we do this?
To isolate the $x$ terms and make it easier to solve for $x$ !

Next, subtract 4 from both sides to get:
$9 = 3x$
Now, we have a simpler equation!
We're getting closer!

Finally, divide both sides by 3 to solve for $x$ :
$x = 3$
And there we have it!
We found the value of $x$ .

The value of $x$ that makes the measures of the vertical angles equal is $x = 3$ .