For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?
Vertical angles are formed by the intersection of two lines. In this case, the vertical angles are angles 2 and 4.
According to the vertical angles theorem, vertical angles are congruent, meaning that they have the same measures.
Therefore, m∠2 = m∠4
We can set up an equation to solve for x:
5x + 23 = 3x + 35
Subtract 3x from both sides:
2x + 23 = 35
Subtract 23 from both sides:
2x = 12
Divide both sides by 2:
x = 6
Now that we have the value of x, we can substitute it back into either equation to find the measures of the angles. Let's use angle 2:
m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53
Therefore, m∠2 = 53°
Since vertical angles are congruent, m∠4 = m∠2 = 53°.