Question

In the given figure, ABCD is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

Answer 1

Answer:

Step-by-step explanation:

z = 30° , x = 110° and y = 40°

Step-by-step explanation:

Given , HOPE is a parallelogram.

i ) <EHO = External angle at O

( Corresponding angles )

=> 40° + z = 70°

=> z = 70° - 40° = 30° ---(1)

ii ) <E + <H = 180°

(Sum of adjacent angles are supplementary )

=> x + 40° + z = 180°

=> x + 40° + 30° = 180° [ From (1) ]

=> x + 70° = 180°

=> x = 180° - 70°

=> x = 110° ------------(2)

iii) z + y= 70°

[ sum of interior opposite angles = Exterior angle]

=> 30° + y = 70° [ From (1) ]

=> y = 70° - 30° = 40° -----(3)

Therefore.,

z = 30° , x = 110° and y = 40°

Answer 2

Answer:

x=100⁰

y=50⁰

z=80⁰

Step-by-step explanation:

because opposite side of parallelogram are equal