Question

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

Answer 1

Answer:

Since HOPE is a parallelogram, therefore, HE || OP and

HO ||

EP

Now, HE || OP and transversal HO intersects them. .. ZEHO = ZP OX. Corresponding angles are equal]

240° + z = 70° ⇒ z = 70° - 40° = 30°

Again, HE || OP and transversal HP intersects them. ..ZOPH = ZEHP Alternate angles

are equal)

⇒ y = 40°

Since opposite angles are equal in a parallelogram.

..ZHEP = ZHOP ⇒ x = 180° - ZPOX = 180° - 70º =

110⁰

Hence, x = 110⁰°, y = 40° and z = 30⁰

Answer 2

Step-by-step explanation:

Since HOPE is a parallelogram, therefore, HE∥OP and

HO∥EP

Now, HE∥OP and transversal HO intersects them.

∴∠EHO=∠POX[∵ Corresponding angles are equal]

∠40

o

+z=70

o

⇒z=70

o

−40

o

=30

o

Again, HE∥OP and transversal HP intersects them.

∴∠OPH=∠EHP[∵ Alternate angles are equal)

⇒y=40

o

Since opposite angles are equal in a parallelogram.

∴∠HEP=∠HOP

⇒x=180

o

−∠POX=180

o

−70

o

=110

o

Hence, x=110

o

,y=40

o

and z=30

o