Question

The adjacent figure HOPE,is a pallelogram . Find the angles measure of x,y and z. state the properties you used to find them.​

Answer 1

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]

∠40o+z=70o⇒z=70o−40o=30o

Again, HE∥OP and transversal HP intersects them.

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

⇒y=40o

Since opposite angles are equal in a parallelogram.

∴∠HEP=∠HOP

⇒x=180o−∠POX=180o−70o=110o

Hence, x=110o,y=40o and z=30o

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