Question

If cos∠E = sin∠F and m∠E = 72°, what is m∠F?

Answer 1

When we have the following relation

$\begin{gathered} \sin(A)=\cos(B) \\ \cos(B)=\sin(A) \end{gathered}$

The angles A and B are complementary. When two angles are complementary, their measures add to 90º.

$\begin{gathered} m\angle E+m\angle F=90 \\ (72)+m\angle F=90 \\ m\angle F=90-72 \\ m\angle F=18 \end{gathered}$

The measure of the angle F is 18º.