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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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