Final answer:
The measure of each angle in a pair of vertical angles, with one angle represented by (3x + 4) and the other by (7x - 9), is 13.75 degrees after solving the equation for x and substituting it back into either expression.
Step-by-step explanation:
We are given a pair of vertical angles where one angle is represented by (3x + 4) and the other is represented by (7x - 9). Since vertical angles are equal, we can set these expressions equal to each other to find the value of x. Starting with the equation 3x + 4 = 7x - 9, we can solve for x. Moving all terms involving x to one side and constants to the other, we get 4 + 9 = 7x - 3x, which simplifies to 13 = 4x. Dividing both sides by 4 gives us x = 13/4 or x = 3.25. To find the measure of each angle, we substitute x back into one of the original expressions: 3(3.25) + 4 which equals 9.75 + 4, or 13.75 degrees. Since they are vertical angles, each angle measures 13.75 degrees.