Question

In the figure HOPE is a parallelogram. Find the measures of angles x, y and z. State the properties used.

Answer 1

Answer:

z=40°

z=80°

y=60°••••••••

Answer 2

( i made ∠PEO  x to avoid confusion)

80°+ (60°+ z) = 180° (Linear Pair)

80° + 60° + z = 180°

140° +z = 180°

z = 180° - 140°

z = 40°

∠POH = 60° + 40°

          = 100°

∠y = 180 - ∠POH  ( adjacent angles are supplementary)

    = 180  - 100

    = 80

In Δ EPO

x + y + 60  = 180  (sum of all angles of a triangle is 180)

x + ( 80 + 60) = 180

x + 140 = 180

x = 180- 140

x = 40

∴ x = 40° , y = 80° and z = 40°