Question

AC ∥ DF, m∠F = 40°What is the m∠FEG?

Answer 1

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Answer:

• m∠EGF = 50°
• m∠D = 40°
• m∠ABE = 90°

Step-by-step explanation:

The drawing is a bit unfortunate, as it does not show the angles true to size.

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When the altitude (EG) of a triangle (∆DFG) is also a median, then that triangle is isosceles. Both halves are congruent right triangles.

  ∆GED ≅ ∆GEF

Since these are right triangles, the acute angle not given (∠EGF) is the complement of the one that is given.

  m∠EGF = 90° -m∠F = 90° -40°

  m∠EGF = 40°

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Of course, angle D in ∆GED is identical to its counterpart in ∆GEF, angle F, so ...

  m∠D = 40°

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Because the lines are parallel, angle ABE corresponds (and is congruent) to angle DEG, which is marked as a right angle.

  m∠ABE = 90°