Question

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 need to set the two expressions for the angles equal to each other and solve for 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 found the value of x, we can substitute it back into either expression to find the measure of each angle.

m∠2 = 5x + 23

m∠2 = 5(6) + 23

m∠2 = 30 + 23

m∠2 = 53 degrees

m∠4 = 3x + 35

m∠4 = 3(6) + 35

m∠4 = 18 + 35

m∠4 = 53 degrees

Therefore, the measure of each angle is 53 degrees.