For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)
Since vertical angles are congruent, we can set the measures of the two vertical angles equal to each other and solve for the value of x:
m∠2 = m∠4
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 into either of the angle measures to find the value of the angle. Let's use m∠2:
m∠2 = 5x + 23
m∠2 = 5(6) + 23
m∠2 = 30 + 23
m∠2 = 53°
Therefore, each angle has a measure of 53 degrees.