For two vertical angles with measures m 2 = (5x + 23) and m 4 = (3x + 35), what is the measure of each angle?
A. 29
B. 15.3
C. 53
D. 6
Vertical angles are opposite angles formed by the intersection of two lines. In this case, angles 2 and 4 are vertical angles.
Since vertical angles are equal, we can set up the following equation:
m2 = m4
5x + 23 = 3x + 35
To solve for x, subtract 3x from both sides of the equation:
5x - 3x + 23 = 3x - 3x + 35
2x + 23 = 35
Then subtract 23 from both sides of the equation:
2x + 23 - 23 = 35 - 23
2x = 12
To solve for x, divide both sides of the equation by 2:
2x/2 = 12/2
x = 6
Now that we have the value of x, we can substitute it back into the expressions for m2 and m4 to find the measure of each angle.
m2 = 5x + 23 = 5(6) + 23 = 30 + 23 = 53
m4 = 3x + 35 = 3(6) + 35 = 18 + 35 = 53
Therefore, the measure of each angle is 53 degrees. The correct answer is C. 53.