Answer:
Based on the information given, we know that angles 3 and 4 are supplementary (they add up to 180 degrees) and angles 2 and 4 are vertical angles (they are congruent). Therefore, we can write:
m∠4 + m∠3 = 180 (since angles 3 and 4 are supplementary)
m∠4 = m∠2 (since angles 2 and 4 are vertical angles)
Substituting m∠4 = m∠2 into the first equation, we get:
m∠2 + m∠3 = 180
Now we can solve for m∠2 and m∠3:
m∠3 = 43 (given)
m∠2 = 180 - m∠3 = 180 - 43 = 137
Since angles 1 and 2 are also supplementary, we can find m∠1 by subtracting m∠2 from 180:
m∠1 = 180 - m∠2 = 180 - 137 = 43
Therefore, m∠1 = 43 degrees and m∠2 = 137 degrees.