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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,\( x = 110^{\circ}, y = 40^{\circ} and\; z = 30^{\circ}.\)

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