Question

Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{required}\mathrm{angle}\mathrm{be}x°. \\ \mathrm{As}\mathrm{the}\mathrm{adjacent}\mathrm{angles}\mathrm{are}\mathrm{equal},\mathrm{we}\mathrm{have}: \\ x+x=180\left(s\mathrm{ince}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°\right) \\ \Rightarrow 2x=180 \\ \Rightarrow x=\frac{180}{2} \\ \Rightarrow x=90° \\ \mathrm{Hence},\mathrm{the}\mathrm{measure}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{angles}\mathrm{is}90°. \end{gathered}$$