Since the angles ∠P and ∠Q are complementary, then:
[tex]∠P+∠Q=90º[/tex]Since ∠P is 40º greater than ∠Q, then:
[tex]∠P=∠Q+40º[/tex]Replace this expression for ∠P in the first equation and solve for ∠Q:
[tex]\begin{gathered} ∠P+∠Q=90º \\ \\ \Rightarrow∠Q+40º+∠Q=90º \\ \\ \Rightarrow2∠Q+40º=90º \\ \\ \Rightarrow2∠Q=50º \\ \\ \therefore∠Q=25º \end{gathered}[/tex]Since ∠P is 40º greater than ∠Q, then ∠P=65º.
Therefore, the measures of the angles ∠P and ∠Q are:
[tex]\begin{gathered} ∠P=65º \\ ∠Q=25º \end{gathered}[/tex]