Final answer:
To find m∠2 - m∠3, we first determine the measures of ∠2 and ∠3. ∠2 is found by subtracting ∠1 from 180, and ∠3 is found by subtracting ∠2 from 90. Finally, we subtract the value of ∠3 from ∠2 to find m∠2 - m∠3.
Step-by-step explanation:
To find the value of m∠2 - m∠3, we need to determine the measures of ∠2 and ∠3. We know that ∠1 is a supplement of ∠2, so the sum of ∠1 and ∠2 is 180 degrees. Since we are given that m∠1 = 115 degrees, we can find m∠2 by subtracting 115 from 180. Thus, m∠2 = 180 - 115 = 65 degrees.
We also know that ∠2 is a complement of ∠3, so the sum of ∠2 and ∠3 is 90 degrees. Substituting the value of m∠2, we can solve for m∠3 by subtracting 65 from 90. Therefore, m∠3 = 90 - 65 = 25 degrees.
Finally, to find m∠2 - m∠3, we subtract the value of m∠3 from m∠2: m∠2 - m∠3 = 65 - 25 = 40 degrees.