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

Answer :

We have, $$∠y = 40^{\circ}$$ (Alternate angles)

$$∠z + 40°^{\circ} = 70^{\circ}$$ (Exterior angle property)

$$\Rightarrow ∠z = 70^{\circ} – 40^{\circ} = 30^{\circ}$$

$$z = ∠EPH \quad$$[Alternate angle]

In ∆EPH, $$∠x + 40^{\circ} + ∠z = 180^{\circ}\quad$$ [Adjacent angles]

$$\Rightarrow ∠x + 40^{\circ} + 30^{\circ} = 180^{\circ}$$

$$\Rightarrow ∠x + 70^{\circ} = 180^{\circ}$$

$$\Rightarrow ∠x = 180^{\circ} – 70^{\circ} = 110^{\circ}$$

Hence we have,$$x = 110^{\circ}, y = 40^{\circ} and\; z = 30^{\circ}.$$