In the adjacent figure HOPE is a parallelogram.

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.

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 $s$ )

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