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

A. 15.3 degrees
B. 53 degrees
C. 29 degrees
D. 6 degrees

1 answer

To find the measure of each angle, we need to set up an equation because vertical angles are congruent.

Given that m2 = (5x + 23) degrees and m4 = (3x + 35) degrees, we can set up the equation:

5x + 23 = 3x + 35

Subtracting 3x from both sides gives:

2x + 23 = 35

Subtracting 23 from both sides gives:

2x = 12

Dividing both sides by 2 gives:

x = 6

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

m2 = 5(6) + 23 = 53 degrees

m4 = 3(6) + 35 = 53 degrees

Therefore, the measure of each angle is 53 degrees. So, the answer is:

B. 53 degrees