Question

In Fig. 17.28, ABCD and AEFG are parallelograms. If ∠C = 55°, what is the measure of ∠F?

Answer 1

$$\begin{gathered} \mathrm{Both}\mathrm{the}\mathrm{parallelograms}\mathrm{ABCD}\mathrm{and}\mathrm{AEFG}\mathrm{are}\mathrm{similar}. \\ \therefore \angle \mathrm{C}=\angle \mathrm{A}=55°(\mathrm{opposite}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{equal}) \\ \therefore \angle \mathrm{A}=\angle F=55°(\mathrm{opposite}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{equal}) \end{gathered}$$