Question

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

Answer 1

$\angle HOP+{70}^{\circ }={180}^{\circ }$
$Here\angle HOP={180}^{\circ }-{70}^{\circ }={110}^{\circ }\left[Anglesoflinearpair\right]And\angle HEP=\angle HOP\left[Oppositeanglesofaparallelogramareequal\right]\Rightarrow x={110}^{\circ }\angle PHE=\angle HPO\left[Alternateangles\right]\therefore y={40}^{\circ }Now\angle EHO=\angle O={70}^{\circ }\left[Correspondingangles\right]\Rightarrow {40}^{\circ }+z={70}^{\circ }\Rightarrow z={70}^{\circ }-{40}^{\circ }={30}^{\circ }Hence,x={110}^{\circ },y={40}^{\circ }andz={30}^{\circ }$