The measure of two verticle angles are 9x + 3 and 12x - 6. Find x.(1 point)
Vertical angles are congruent, meaning they have the same measure. Therefore, we can set the two expressions equal to each other and solve for x:
9x + 3 = 12x - 6
Subtract 9x from both sides:
3 = 3x - 6
Add 6 to both sides:
9 = 3x
Divide both sides by 3:
x = 3
Therefore, x = 3.
To find the value of x, we need to set the two vertical angles equal to each other and solve for x.
Given:
Vertical angle 1: 9x + 3
Vertical angle 2: 12x - 6
Setting them equal to each other, we have the equation:
9x + 3 = 12x - 6
Now, let's solve for x step by step:
Step 1: Combine like terms by subtracting 9x from both sides:
9x - 9x + 3 = 12x - 9x - 6
3 = 3x - 6
Step 2: Add 6 to both sides to isolate the x-term:
3 + 6 = 3x - 6 + 6
9 = 3x
Step 3: Divide both sides by 3 to solve for x:
9/3 = (3x)/3
3 = x
Therefore, the value of x is 3.
To find the value of x, we can set the two vertical angles equal to each other and solve for x.
According to the given information, the measure of the first vertical angle is 9x + 3, and the measure of the second vertical angle is 12x - 6.
So, we can set up the equation:
9x + 3 = 12x - 6
To solve this equation, we first want to get rid of the variable terms on one side. In this case, we can subtract 9x from both sides of the equation:
(9x + 3) - 9x = (12x - 6) - 9x
This simplifies to:
3 = 3x - 6
Next, we want to isolate the variable term. We can do this by adding 6 to both sides of the equation:
3 + 6 = 3x - 6 + 6
This simplifies to:
9 = 3x
Finally, we can solve for x by dividing both sides of the equation by 3:
9/3 = (3x)/3
This simplifies to:
3 = x
Therefore, x is equal to 3.