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

Answer 1

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.