Answer
1. Given
2. Definition of the supplementary angle
3. Substraction Property of Inequality
4. Addition Property of Inequality
5. Definition of an obtuse angle
Work Step by Step
1. If $\angle1$ is acute and $m\angle1=x$ then $0\lt x\lt 90$
2. The supplementary angle of $\angle 1$ is $\angle2$ and $m\angle2=y$. Therefore $x+y=180$
3. $-x\lt 0\lt 90-x$ (We substract $x$ from all three sides of the inequality in statement (1.))
4. $90-x\lt 90\lt 180-x$ (We add 90 to all three sides of the inequality in statement(3.))
5. $180-x=y$ and $90\lt 180-x\lt 180$ ( because $x$ is positive), which is the definition of an obtuse angle, we can conclude, that $\angle2$ is an obtuse angle.