Let the measure of the angle be \( x \) degrees. The measure of its complementary angle, which adds up with \( x \) to 90 degrees, will be \( 90 - x \) degrees.
According to the problem, the measure of the angle \( x \) is three times the measure of its complementary angle:
\[ x = 3(90 - x) \]
Now, let's solve the equation:
\[ x = 270 - 3x \]
Next, we will add \( 3x \) to both sides:
\[ x + 3x = 270 \]
This simplifies to:
\[ 4x = 270 \]
Now, divide both sides by 4:
\[ x = \frac{270}{4} = 67.5 \]
Now we can find the measure of the complementary angle:
\[ 90 - x = 90 - 67.5 = 22.5 \]
Thus, the measures of the angles are:
- The angle is \( 67.5^\circ \)
- The complementary angle is \( 22.5^\circ \)
In summary, the measures of the angles are \( 67.5^\circ \) and \( 22.5^\circ \).