Final answer:
To find the value of x, we need to set up an equation using the fact that vertical angles are equal. The measure of angle 1 is (6x + 29)° and the measure of angle 2 is (7x + 25)°. Setting them equal and solving for x gives x = 4.
Step-by-step explanation:
To find the value of x, we need to set up an equation using the fact that vertical angles are equal. The measure of angle 1 is given as (6x + 29)° and the measure of angle 2 is given as (7x + 25)°. Since angle 1 and angle 2 are vertical angles, they are equal, so we can equate them: (6x + 29)° = (7x + 25)°.
To solve for x, we need to isolate the variable on one side of the equation. First, let's simplify the equation: 6x + 29 = 7x + 25. Next, let's move the variable terms to one side and the constant terms to the other side: 29 - 25 = 7x - 6x. This simplifies to 4 = x. Therefore, the value of x is 4.