For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?
15.3°
29°
53°
6°
Since vertical angles are congruent, we can set the two angles equal to each other and 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 we can substitute x = 6 back into one of the angle measures to find the measure of each angle:
m∠2 = 5(6) + 23 = 53°
m∠4 = 3(6) + 35 = 53°
Therefore, the measure of each angle is 53°.