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

Lines AB and CD are parallel. Find the measures of the three angles in triangle ABF-example-1

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Answer:

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°

User Lachlan Cotter
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