For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point) Responses 53 6 15.3 29
Since the angles are vertical angles, they are congruent. Therefore, the measure of angle 2 is equal to the measure of angle 4.
Setting them equal to each other:
5x + 23 = 3x + 35
Subtracting 3x from both sides:
2x + 23 = 35
Subtracting 23 from both sides:
2x = 12
Dividing both sides by 2:
x = 6
Substituting x back into the equations for angle 2 and angle 4:
m∠2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53°
m∠4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53°
Therefore, the measure of each angle is 53 degrees.