since vertical angles are equal,
5x-54 = 3x-24
2x = 30
x = 15
The angles are 21 degrees
If a pair of vertical angles measures 5x - 54 and 3x -24, find the measures of the angles.
5x-54 = 3x-24
2x = 30
x = 15
The angles are 21 degrees
Let's use the given expressions for the measures of the vertical angles:
Angle 1: 5x - 54
Angle 2: 3x - 24
Since vertical angles are congruent, we can set up an equation to find the value of x:
5x - 54 = 3x - 24
Now, let's solve this equation:
5x - 3x = -24 + 54
2x = 30
x = 15
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures:
Angle 1: 5x - 54 = 5(15) - 54 = 75 - 54 = 21
Angle 2: 3x - 24 = 3(15) - 24 = 45 - 24 = 21
Therefore, the measures of the angles are both 21 degrees.
So, we have:
5x - 54 = 3x - 24
Now, we will solve this equation for x:
5x - 3x = -24 + 54
2x = 30
x = 30/2
x = 15
Now that we have the value of x, we can substitute it back into either expression to find the measures of the angles.
Let's use the first expression:
Angle 1 = 5x - 54 = 5(15) - 54 = 75 - 54 = 21
Therefore, the measure of the first angle is 21 degrees.
To find the measure of the second angle, we can substitute x = 15 into the second expression:
Angle 2 = 3x - 24 = 3(15) - 24 = 45 - 24 = 21
Therefore, the measure of the second angle is also 21 degrees.
So, both angles measure 21 degrees.