Question

Given the figure, HOPE is a parallelogram. Find the measure of the angles x, y and z.

Answer 1

$\angle HOP+{70}^{\circ }={180}^{\circ }\left[linearpair\right]\Rightarrow \angle HOP={180}^{\circ }-{70}^{\circ }={110}^{\circ }$
because Opposite angles of a parallelogram are equal
$\therefore x=\angle HOP={110}^{\circ }\angle EHO+\angle HEP={180}^{\circ }$
[Sum of adjacet angles of a parallelogram is ${180}^{\circ }$]
$\Rightarrow z^{\circ }+{40}^{\circ }+x^{\circ }={180}^{\circ }\Rightarrow z^{\circ }+{40}^{\circ }+{110}^{\circ }={180}^{\circ }\Rightarrow z^{\circ }={180}^{\circ }-{150}^{\circ }={30}^{\circ }{y}^{\circ }=\angle EHP={40}^{\circ }\left[alternateangles\right]\therefore x\circ =110\circ y^{\circ }={40}^{\circ }{z}^{\circ }={30}^{\circ }$