If angle symbol1 and angle symbol2 are complementary angles and if the measure of angle symbol1 is 5454degrees° more than the measure of angle symbol 2, 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.