1. **State the problem:** We need to find two complementary angles where one angle is forty-four times the other. 2. **Recall the definition of complementary angles:** Two angles are complementary if their measures add up to 90 degrees. 3. **Set variables:** Let the smaller angle be $x$ degrees. 4. **Express the other angle:** The other angle is $44x$ degrees. 5. **Write the equation for complementary angles:** $$x + 44x = 90$$ 6. **Simplify the equation:** $$45x = 90$$ 7. **Solve for $x$:** $$x = \frac{90}{45}$$ $$x = 2$$ 8. **Find the other angle:** $$44x = 44 \times 2 = 88$$ 9. **Answer:** The two angles are $2^\circ$ and $88^\circ$. These angles add up to 90 degrees and satisfy the condition that one is forty-four times the other.