Question 1145297
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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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<U>Solution</U>


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 


<U>ANSWER</U>.  Angle GEF measure is 3*8 = 24 degrees;  angle GED measure is 5*8 = 40 degrees.


<U>CHECK</U>.  {{{24/40}}} = {{{3/5}}}.    ! Correct !
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Solved.