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..png)
Solution:
$\angle \mathrm{HOP}+70^{\circ}=180^{\circ} \quad(l$ inear pair $)$
$\angle \mathrm{HOP}=180^{\circ}-70^{\circ}=110^{\circ}$
$\mathrm{x}=\angle \mathrm{HOP}=110^{\circ}(o$ pposite angles of a parallelogram are equal $)$
$\angle \mathrm{EHP}+\angle \mathrm{HEP}=180^{\circ} \quad\left(s\right.$ um of adjacent angles of a parallelogram is $\left.180^{\circ}\right)$
$110^{\circ}+40^{\circ}+\mathrm{z}=180^{\circ}$
$\mathrm{z}=180^{\circ}-150^{\circ}=30^{\circ}$
$\mathrm{y}=40^{\circ}$ (alternate angle $s$ )