Question

In the adjacent figure HOPE is a parallelogram. Find the angle measures x,y and z. State the geometrical truths you use to find them.

Answer 1

$$\begin{gathered} \angle \mathrm{HOP}+70°=180°(l\mathrm{inear}\mathrm{pair}) \\ \angle \mathrm{HOP}=180°-70°=110° \\ \mathrm{x}=\angle \mathrm{HOP}=110°(o\mathrm{pposite}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{are}\mathrm{equal}) \\ \angle \mathrm{EHP}+\angle \mathrm{HEP}=180°(s\mathrm{um}\mathrm{of}\mathrm{adjacent}\mathrm{angles}\mathrm{of}\mathrm{a}\mathrm{parallelogram}\mathrm{is}180°) \\ 110°+40°+\mathrm{z}=180° \\ \mathrm{z}=180°-150°=30° \\ \mathrm{y}=40°\left(\mathrm{alternate}\mathrm{angle}s\right) \end{gathered}$$