Final answer:
Vertical angles are equal, so by setting the expressions for angle 1 and angle 2 equal and solving for x, we find that the measure of angle 2 is 95 degrees.
Step-by-step explanation:
The problem involves equal vertical angles. If the measure of angle 1 is 2x+25 and the measure of angle 2 is 3x-10, and since vertical angles are equal in measure, we set 2x+25 equal to 3x-10 to find the value of x, and then solve for the measure of angle 2.
To find x, we rearrange the equation 2x + 25 = 3x - 10 by subtracting 2x from both sides and adding 10 to both sides, leading to x = 35. Then we substitute x in the expression for angle 2:
Angle 2 = 3x - 10
Angle 2 = 3(35) - 10 = 105 - 10 = 95 degrees.