an angle measures 58 degrees more than the measure of a complementary angle what is the measure of each angle

Let the first angle be x.  Then the second angle can be represented by (90-x)+58.  We then have 

x = (90-x)+58.  Simplifying, x = 90 - x + 58

Then 2x = 90+58, or 2x = 148, or x = 74 degrees.

The first angle is 74 deg.  I am assuming that we find the complement of this 74 and then add 58 deg.  Unfortunately, that results in 74 deg.  Seems like we're going around in circles.

Please reread the original problem statement.  To me, it's vague where it mentions "the measure of a complementary angle."  I assumed that it really meant "the measure of the complement to "an angle," i. e., "the measure of the complement of 74 deg."

Could someone else shed light on this problem's wording and solution?