Question

The below figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Answer 1

$\angle y={40}^{\circ }\left(\text{Alternate angles}\right)$
$\angle z+{40}^{\circ }={70}^{\circ }\text{(Exterior angle property)}$
$\Rightarrow \angle z={70}^{\circ }-{40}^{\circ }={30}^{\circ }$
$z=\angle EPH\text{(Alternate angle)}$
In$\Delta EPH,\angle x+{40}^{\circ }+\angle z={180}^{\circ }\text{(Adjacent angles)}$
$\Rightarrow \angle x+{40}^{\circ }+{30}^{\circ }={180}^{\circ }$
$\Rightarrow \angle x+{70}^{\circ }={180}^{\circ }$
$\Rightarrow \angle x={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
$Hencex={110}^{\circ },y={40}^{\circ }andz={30}^{\circ }.$