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julsineya
14 days ago
13

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

Mathematics
1 answer:
Svet_ta [9.4K]14 days ago
3 0

Response:    ∠B = 42°   ∠A = 23°  ∠F = 115°

Detailed explanation:

∠B is congruent to ∠C  alternate interior angles  42°

  ∠CDF is supplementary to ∠CDE,

thus m∠CDF = 23°  and ∠FAB is congruent to ∠CDF therefore m∠FAB= 23°

also ∠A is congruent to ∠CDE  corresponding angles  157° ∠FAB is supplementary to ∠A

which leads to 180 - 157 = 23 giving m∠FAB

The sum of angles in a triangle amounts to 180°, so m∠AFB = 180 -(23 +42)

This results in 180- 65 = 115 = m∠F

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