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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°
