Question

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

6°6 degrees

15.3°15.3 degrees

53°
53 degrees

29°

Answer 1

To find the measure of each angle, we can set their measures equal to each other, as vertical angles are congruent:

m∠2 = m∠4
(5x + 23)° = (3x + 35)°

Now, we can solve for x:

5x + 23 = 3x + 35
5x - 3x = 35 - 23
2x = 12
x = 6

Now that we have found x, we can substitute it back into either equation to find the measure of each angle:

m∠2 = 5(6) + 23 = 30 + 23 = 53

m∠4 = 3(6) + 35 = 18 + 35 = 53

Therefore, the measure of each angle is 53°.