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.

Question

Philoid · Accepted Answer

∠HOP + 70° = 180° [Linear pair]

∠HOP = 180°-70°

∠HOP = 110°

∠HOP = ∠x = 110° [In a parallelogram opposite angles are equal]

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

110° + ∠z + 40° = 180°

∠z = 180° - 150°

∠z = 30°

∠z +∠y = 70°

∠y + 30° = 70°

∠y = 70°- 30°

∠y = 40°