Math / Geometry

QuestionSolve for $x$ : $x=\square$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ given two vertical angles. Watch out! Don't forget that vertical angles are equal!

STEP 2

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

STEP 3

Alright, so we've got these two angles staring at each other!
They're called vertical angles, and guess what?
Vertical angles are always equal!
So, let's write that down!

STEP 4

Our first angle is $6x + 34^\circ$ and our second angle is $8x + 14^\circ$ .
Since they're equal, we can write the equation: $6x + 34 = 8x + 14$

STEP 5

Isolate the $x$ terms!
Let's subtract $6x$ from both sides of the equation.
Remember, what we do to one side, we gotta do to the other!
This keeps everything nice and balanced. $6x + 34 - 6x = 8x + 14 - 6x$ $34 = 2x + 14$ See how the $6x$ on the left side adds to zero with $-6x$ ?
Awesome!

STEP 6

Now, let's subtract 14 from both sides to get those $x$ terms all alone! $34 - 14 = 2x + 14 - 14$ $20 = 2x$ Again, we added 14 to -14 to get zero on the right side.
Perfect!

STEP 7

Almost there!
We want to find the value of a single $x$ , not $2x$ .
So, let's divide both sides by 2! $\frac{20}{2} = \frac{2x}{2}$ $10 = x$ We divided 2 by 2 to get one on the right side.
Boom!

STEP 8

We found that $x = 10$ .
Woohoo!

Was this helpful?

QuestionSolve for $x$ : $x=\square$

Studdy Solution

STEP 1

What is this asking? We need to find the value of $x$ given two vertical angles. Watch out! Don't forget that vertical angles are equal!

STEP 2

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

STEP 3

Alright, so we've got these two angles staring at each other!
They're called vertical angles, and guess what?
Vertical angles are always equal!
So, let's write that down!

STEP 4

Our first angle is $6x + 34^\circ$ and our second angle is $8x + 14^\circ$ .
Since they're equal, we can write the equation: $6x + 34 = 8x + 14$

STEP 5

Isolate the $x$ terms!
Let's subtract $6x$ from both sides of the equation.
Remember, what we do to one side, we gotta do to the other!
This keeps everything nice and balanced. $6x + 34 - 6x = 8x + 14 - 6x$ $34 = 2x + 14$ See how the $6x$ on the left side adds to zero with $-6x$ ?
Awesome!

STEP 6

Now, let's subtract 14 from both sides to get those $x$ terms all alone! $34 - 14 = 2x + 14 - 14$ $20 = 2x$ Again, we added 14 to -14 to get zero on the right side.
Perfect!

STEP 7

Almost there!
We want to find the value of a single $x$ , not $2x$ .
So, let's divide both sides by 2! $\frac{20}{2} = \frac{2x}{2}$ $10 = x$ We divided 2 by 2 to get one on the right side.
Boom!

STEP 8

We found that $x = 10$ .
Woohoo!

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.

QuestionSolve for xxx : x=□x=\squarex=□

Studdy Solution

STEP 1

What is this asking? We need to find the value of xxx given two vertical angles. Watch out! Don't forget that vertical angles are equal!

STEP 2

1. Set up the equation2. Solve for xxx

STEP 3

Alright, so we've got these two angles staring at each other!They're called **vertical angles**, and guess what?Vertical angles are **always equal**!So, let's write that down!

STEP 4

Our first angle is 6x+34∘6x + 34^\circ6x+34∘ and our second angle is 8x+14∘8x + 14^\circ8x+14∘.Since they're equal, we can write the equation: 6x+34=8x+146x + 34 = 8x + 146x+34=8x+14

STEP 5

STEP 6

Now, let's **subtract** 14 from both sides to get those xxx terms all alone! 34−14=2x+14−1434 - 14 = 2x + 14 - 1434−14=2x+14−14 20=2x20 = 2x20=2xAgain, we added 14 to -14 to get zero on the right side.Perfect!

STEP 7

Almost there!We want to find the value of a **single** xxx, not 2x2x2x.So, let's **divide** both sides by 2! 202=2x2\frac{20}{2} = \frac{2x}{2}220​=22x​ 10=x10 = x10=xWe divided 2 by 2 to get one on the right side.Boom!

STEP 8

We found that x=10x = 10x=10.Woohoo!

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.

QuestionSolve for $x$ : $x=\square$

What is this asking? We need to find the value of $x$ given two vertical angles. Watch out! Don't forget that vertical angles are equal!

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

Alright, so we've got these two angles staring at each other!
They're called vertical angles, and guess what?
Vertical angles are always equal!
So, let's write that down!

Our first angle is $6x + 34^\circ$ and our second angle is $8x + 14^\circ$ .
Since they're equal, we can write the equation: $6x + 34 = 8x + 14$

Now, let's subtract 14 from both sides to get those $x$ terms all alone! $34 - 14 = 2x + 14 - 14$ $20 = 2x$ Again, we added 14 to -14 to get zero on the right side.
Perfect!

Almost there!
We want to find the value of a single $x$ , not $2x$ .
So, let's divide both sides by 2! $\frac{20}{2} = \frac{2x}{2}$ $10 = x$ We divided 2 by 2 to get one on the right side.
Boom!

We found that $x = 10$ .
Woohoo!