In the figure, HOPE is a parallelogram. Find the measure of angle x, y and z.
E
x
P Р
40°
Rz
1
70°
H
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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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