## Elementary Geometry for College Students (5th Edition)

1. Given 2. The definition of complementary angles 3. Given 4. The definition of an acute angle 5. Substituting $m\angle 1$ in the equation (Statement 2.) 6. Subtracting $x$ from both sides. 7. Subtracting $x$ from all three sides in the inequality (Statement 4.) 8. Adding $90$ to all three sides in the equality (Statement 7.) 9. Transitive property of inequality (Statement 7. and 8.) As $0\lt 90-x$ and $90-x\lt90$, therefore $0\lt90-x\lt90$ 10. Substituting $90-x$ by $m\angle 2$ (Statement 6.) 11. Using the definition of an acute angle