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

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

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The adjacent figure HOPE is a parallelogram.

$\angle HOP +70\degree = 180\degree$           (linear pairs)

$\angle HOP = 110\degree$

$x= \angle HOP = 110\degree$              (opposite angles of parallelogram are equal)

$\angle HOP +\angle EHO = 180\degree$   ( adjacent angles are supplemantary )

$110\degree +(40\degree+z) = 180\degree$

$z = 180\degree - 150\degree$

$z = 30\degree$

y= $40\degree$                       (Alternate interior angles are equal)

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