For two vertical angles with measures m∠2=(5x+23)° and m∠4=(3x+35)° , what is the measure of each angle?(1 point)

Question

Responses

53°
53 degrees

6°
6 degrees

29°
29 degrees

15.3°

Answer 1

To find the measure of each angle, we need to set the measures of the two angles equal to each other:

m∠2 = m∠4

(5x+23)° = (3x+35)°

Now, we can solve for x:

5x+23 = 3x+35

2x+23 = 35

2x = 12

x = 6

Using this value of x, we can find the measure of each angle:

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. Answer: \boxed{53°}.