Question

The adjacent figure HOPE 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.

∴∠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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