he adjacent figure ABCD is a parallelogram. Find the angle measures x, y, z. State the properties you use to find them.
(4 Points)
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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
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