Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF.

m(∠FBA) = 42°

m(∠FAB) = 23°

m(∠AFB) = 115°

Step-by-step explanation:

Lines AB and CD are parallel.

m(∠FCD) = m(∠FBA) = 42° [Alternate interior angles]

m(∠CDF) + m(∠CDE) = 180° [Linear pair of angles]

m(∠CDF) = 180° - 157°

               = 23°

m(∠CDF) = m(∠BAF) = 23° [Alternate interior angles]

m(∠AFB) + m(∠FBA) + m(∠BAF) = 180° [Sum of interior angles of a triangle]

m(∠AFB) + 42° + 23° = 180°

m(∠AFB) = 180° - 65°

               = 115°

Therefore, m(∠FBA) = 42°

                  m(∠FAB) = 23°

                  m(∠AFB) = 115°

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.