Question

What is the measure of two complementary angles ∠P and ∠Q, if the measure of ∠P is 40° greater than the measure of ∠Q?

Answer 1

Since the angles ∠P and ∠Q are complementary, then:

`∠P+∠Q=90º`

Since ∠P is 40º greater than ∠Q, then:

`∠P=∠Q+40º`

Replace this expression for ∠P in the first equation and solve for ∠Q:

`\begin{gathered} ∠P+∠Q=90º \\ \\ \Rightarrow∠Q+40º+∠Q=90º \\ \\ \Rightarrow2∠Q+40º=90º \\ \\ \Rightarrow2∠Q=50º \\ \\ \therefore∠Q=25º \end{gathered}`

Since ∠P is 40º greater than ∠Q, then ∠P=65º.

Therefore, the measures of the angles ∠P and ∠Q are:

`\begin{gathered} ∠P=65º \\ ∠Q=25º \end{gathered}`