Question

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

Answer 1

$\begin{gathered}\bold {Given}\begin{cases}\sf A\ Quadrilateral\ HOPE\ is\ Parallelogram\\ \sf\angle EHP = 40°\\\sf\angle O = 70°\\\sf\angle HEP = x\\\sf\angle HPO = y\\\sf\angle PHO = z\end{cases}\end{gathered}$

To Find

• Measure of angle x , y , z

Now,

• By corresponding angles

therefore,

$\sf{ ~~~~~ \angle EHO = \angle O }$

$\sf{ ~~~~~ →40+ z = 70 }$

$\sf{ ~~~~~ →z=70-40 }$

$\bf{ ~~~~~ →z=30° }$

Now

• By Exterior angle Property

$\sf{ ~~~~~ →\angle z + \angle y = \angle O }$

$\sf{ ~~~~~ →30 + y = 70 }$

$\sf{ ~~~~~ →y= 70-30 }$

$\bf{ ~~~~~ →y= 40 }$

Now

• By Co- Interior angle

$\sf{ ~~~~~ →\angle HEP + \angle EHO = 180° }$

$\sf{ ~~~~~ →x+40+30= 180 }$

$\sf{ ~~~~~ →x+70=180 }$

$\sf{ ~~~~~ →x= 180-70 }$

$\bf{ ~~~~~ →x = 110° }$

$\sf{ }$

• Hance the Value of x , y , z is 110° , 30° , 40°