Final answer:
The sum of the two vertical angles (4x - 7) and (2x - 13) is 33 degrees.
Step-by-step explanation:
To find the sum of the two vertical angles, we need to equate the expressions representing the measures of the angles and solve for x.
(4x - 7) = (2x - 13)
4x - 7 = 2x - 13
2x = -6
x = -3
Now we can substitute x = -3 back into one of the expressions to find the angle measures.
Angle 1 = (4x - 7) = (4(-3) - 7) = -12 - 7 = -19
Angle 2 = (2x - 13) = (2(-3) - 13) = -6 - 13 = -19
The sum of the two angle measures is: -19 + -19 = -38
Since angle measures cannot be negative, we can conclude that the sum of the two angle measures is 38 degrees. Answer choice (c) 66 is incorrect because the sum is not positive. The correct answer is (a) 33 degrees.