Final answer:
To find the measure of ∠ B, we first establish that ∠ A and ∠ B are supplementary and thus add up to 180 degrees. After setting up the equation (x+15) + (x-13) = 180 and solving for x, we substitute back to find the measure of ∠ B, which is 76 degrees.
Step-by-step explanation:
If ∠ A and ∠ B are supplementary angles, we know that they add up to 180 degrees. Given that m ∠ A = (x+15) and m ∠ B = (x-13), we can write the equation for supplementary angles as follows:
(x+15) + (x-13) = 180
Solving for x:
2x + 2 = 180
2x = 178
x = 89
Now that we have the value of x, we can find m ∠ B by plugging x into the expression given for m ∠ B:
m ∠ B = (89 - 13)
m ∠ B = 76 degrees
Therefore, the measure of ∠ B is 76 degrees.