By leveraging the supplementary relationship of angles 1 and 3, solving for x, and recognizing the vertical angles property, we determine that m(angle 2) is 56 degrees.
Angle 1 and angle 3 are supplementary angles. This means that together, they add up to 180 degrees. We can use this to write down an equation:
m(angle 1) + m(angle 3) = 180 degrees
We are given that m(angle 1) = (2x + 28) degrees and m(angle 3) = (6x + 4) degrees. Substituting these values into the equation, we get:
(2x + 28) degrees + (6x + 4) degrees = 180 degrees
Simplifying the equation, we get:
8x + 32 = 180 degrees
Subtracting 32 from both sides, we get:
8x = 148 degrees
Dividing both sides by 8, we get:
x = 18 degrees
Now that we know the value of x, we can find m(angle 2) using the fact that angle 1 and angle 2 are vertical angles. Vertical angles are angles that are opposite each other and have the same measure. Therefore, m(angle 2) = m(angle 1).
Substituting the value of x that we found earlier, we get:
m(angle 2) = 2 * 18 degrees + 28 degrees
Simplifying the equation, we get:
m(angle 2) = 56 degrees
Therefore, m(angle 2) = 56 degrees.