Let the measure of the first angle be \( x \) degrees and the measure of the second angle be \( y \) degrees. Since the angles are complementary, we have the equation:
\[ x + y = 90 \]
We are also given that the first angle is 30 degrees greater than the second angle:
\[ x = y + 30 \]
Now, we can substitute the expression for \( x \) from the second equation into the first equation:
\[ (y + 30) + y = 90 \]
This simplifies to:
\[ 2y + 30 = 90 \]
Now, we can solve for \( y \):
\[ 2y = 90 - 30 \] \[ 2y = 60 \] \[ y = 30 \]
Now that we have \( y \), we can find \( x \):
\[ x = y + 30 = 30 + 30 = 60 \]
Thus, the measures of the complementary angles are:
- First angle (x): \( 60 \) degrees
- Second angle (y): \( 30 \) degrees
In conclusion, the two complementary angles are \( 60 \) degrees and \( 30 \) degrees.
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