Final answer:
To find the measure of angle 2, we use the properties of linear pairs and vertical angles. Angle 2 equals the measure of angle 3 because they are vertical angles, and their measures must sum to 180 degrees with angle 1 since they are a linear pair. Solving the resulting equation, we find that the measure of angle 2 is 95 degrees.
Step-by-step explanation:
To find the measure of angle 2, we apply our understanding of linear pairs and vertical angles. Angles in a linear pair are supplementary, meaning they add up to 180 degrees. Since angle 1 and angle 2 form a linear pair, their measures add up to 180 degrees. This can be represented as (3y + 10) + measure of angle 2 = 180. Vertical angles, on the other hand, are equal in measure. Thus, angle 2 being a vertical angle to angle 3 means measure of angle 2 = (5y - 30) degrees.
From these relationships, we can set up an equation: (3y + 10) + (5y - 30) = 180. This simplifies to 8y - 20 = 180. We can solve for y by adding 20 to both sides of the equation to get 8y = 200, and then divide both sides by 8 to find y = 25. Substituting 25 for y in the expression for angle 2 gives us (5(25) - 30), which simplifies to 125 - 30 and finally results in 95 degrees as the measure of angle 2.