In the adjacent figure HOPE is a parallelogram. Find the angle measu

1.	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.
Answer» We know that ∠POH + 70° = 180° [Linear pair] ∠POH = 180°-70° ∠POH = 110° ∠POH = ∠x = 110° [opposite angles are equal in a parallelogram] ∠x + ∠z + 40° = 180° [sum of the adjacent angles is equal to 180° in a parallelogram] 110° + ∠z + 40° = 180° ∠z = 180° – 150° ∠z = 30° ∠z +∠y = 70° ∠y + 30° = 70° ∠y = 70°- 30° ∠y = 40°

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.

Answer»

We know that

∠POH + 70° = 180° [Linear pair]

∠POH = 180°-70°

∠POH = 110°

∠POH = ∠x = 110° [opposite angles are equal in a parallelogram]

∠x + ∠z + 40° = 180° [sum of the adjacent angles is equal to 180° in a parallelogram]

110° + ∠z + 40° = 180°

∠z = 180° – 150°

∠z = 30°

∠z +∠y = 70°

∠y + 30° = 70°

∠y = 70°- 30°

∠y = 40°