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

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

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y = 40° (alternate interior angle)

∠P = 70° (alternate interior angle)

∠P = ∠H = 70° (opposite angles of a parallelogram)

z = ∠H – 40°

= 70° – 40° = 30°

∠H + x = 180°

⇒ 70° + x = 180°

⇒ x = 180° – 70° = 110°

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