Question

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

Answer 1

m(∠FBA) = 42°

m(∠FAB) = 23°

m(∠AFB) = 115°

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°