if one of the two vertical angles has a measure of 3x and the other has a measure of 5x - 80. Find the measure of each.
since vertical angles are equal,
3x = 5x-80
3x+5x = 8x
80÷8
10 is the answer
Well, well, well, it seems we have some vertical angles trying to measure up, huh? Let's get to the bottom of this!
We know that vertical angles are congruent, meaning they have the same measure. So, we can set up an equation to solve for x:
3x = 5x - 80
Now, let's bring those x's together:
2x = 80
Dividing both sides by 2, we get:
x = 40
Ah, now we know the value of x!
To find the measure of each angle, let's substitute x back into the expressions:
Angle 1: 3x = 3(40) = 120 degrees
Angle 2: 5x - 80 = 5(40) - 80 = 200 - 80 = 120 degrees
Tada! They both measure 120 degrees. Vertical angles, checkmate!
To find the measure of each vertical angle, we can set these two expressions equal to each other and solve for x.
Given:
Angle 1 measure = 3x
Angle 2 measure = 5x - 80
Setting them equal:
3x = 5x - 80
Now, let's solve for x.
3x - 5x = -80
-2x = -80
Dividing both sides by -2, we get:
x = (-80) / (-2)
x = 40
Now that we have the value of x, we can substitute it back into either of the angle measures to find the actual angle values.
Using Angle 1 measure:
Angle 1 measure = 3x
= 3 * 40
= 120
Using Angle 2 measure:
Angle 2 measure = 5x - 80
= 5 * 40 - 80
= 200 - 80
= 120
Therefore, the measure of each vertical angle is 120 degrees.
To find the measure of each vertical angle, we can set up an equation since we know that vertical angles are congruent.
Let's call the measure of the first angle 3x, and the measure of the second angle 5x - 80.
Since vertical angles are congruent, we can set up the equation:
3x = 5x - 80
To solve for x, we need to isolate the variable on one side of the equation. Let's do that:
3x - 5x = -80
Combine like terms:
-2x = -80
Divide both sides of the equation by -2 to solve for x:
x = -80 / -2
Simplifying:
x = 40
Now that we have the value of x, we can substitute it back into our expressions for the angles.
The measure of the first angle is 3x, so plugging in x = 40:
First angle = 3(40) = 120
The measure of the second angle is 5x - 80, plugging in x = 40:
Second angle = 5(40) - 80 = 200 - 80 = 120
Therefore, the measure of each vertical angle is 120 degrees.