1. **State the problem:** We are given that the measure of an angle is five times the measure of its complementary angle. We need to find the measures of both angles. 2. **Recall definitions and formulas:** - Complementary angles add up to 90 degrees. - If we let the measure of the smaller angle be $x$, then the larger angle is $5x$. 3. **Set up the equation:** Since the angles are complementary, $$x + 5x = 90$$ 4. **Simplify the equation:** $$6x = 90$$ 5. **Solve for $x$:** $$x = \frac{90}{6}$$ 6. **Show cancellation step:** $$x = \cancel{\frac{90}{6}} = 15$$ 7. **Find the larger angle:** $$5x = 5 \times 15 = 75$$ 8. **Answer:** The two complementary angles measure $15^\circ$ and $75^\circ$ respectively.