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It is strange formulation of the problem :
- You call the same angle GEF and FEG by two different names;
- you call the same angle GED and DEG by two different names.
Do you make it intentionally to transform a simple problem into more complicated ?
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Solution
Since the ratio of two angles GEF to GED is 3:5, you can write
m(GEF) = 3x and m(GED) = 5x.
where x is their common angular measure.
Then 3x + 5x = 8x = 64; hence x = 64/8 = 8 degrees.
From it, there is only one step to the
ANSWER. Angle GEF measure is 3*8 = 24 degrees; angle GED measure is 5*8 = 40 degrees.
CHECK. = . ! Correct !
Solved.