Question

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

Answer 1

Finding the required angle:

Given the figure,$HOPE$ is a parallelogram.

Step 1- Finding the value of the angle $y$

$\because EP\parallel OH,HP$ is transversal

$\Rightarrow y=40°$ (alternate interior angle)

Step 2- Finding the value of the angle $z$

$\because EP\parallel OH,OP$ is transversal

$\angle EPO=70°$ (alternate interior angle)

$\angle EPO=\angle EHO$ (opposite angles of a parallelogram)

$$\begin{gathered} \Rightarrow 70=40+Z \\ \Rightarrow Z=70-40 \\ \Rightarrow Z=30° \end{gathered}$$

Step 3 - Finding the value of the angle $x$

$\because EP\parallel OH$

$\Rightarrow \angle PEH+\angle EHO=180°$ (linear pair)

$\Rightarrow x+70=180$

$\Rightarrow x=180-70$

$\Rightarrow x=110°$

Hence, the angle measures are $x=110°,y=40°,z=30°$.