If angle symbol1 and angle symbol2 are complementary angles and if the measure of angle symbol1 is 5454degrees° more than the measure of angle symbol2, determine the measures of angle symbol1 and angle symbol2

Complementary angles by definition sum up to 90 degrees.
   Let x = measure of angle2.
 It's given that angle1 = x + 54

   Since complementary, we know (x+54)+x = 90
 2x+54=90
 2x=36
 x=18.
 So angle2 measures 18 degrees and angle1 is 18 degrees+54 degrees, or 72 degrees. 72+18 = 90 as expected for complementary angles.

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