Answer
1. Given
2. Definition
3. Given
4. Definition
5. Substitution
6. Substraction Property of Equality.
7. Substraction Property of Inequality
8. Addition Property of Equality
9. Transitive property of Inequality
10. Substitution
11. Definition
Work Step by Step
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
