Question

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

• A. 110${}^{\circ }$, 40${}^{\circ }$ and 30${}^{\circ }$
• B. 30${}^{\circ }$, 40${}^{\circ }$ and 60 ${}^{\circ }$
• C. 90${}^{\circ }$, 70${}^{\circ }$ and 80${}^{\circ }$
• D. 80${}^{\circ }$, 20${}^{\circ }$ and 60${}^{\circ }$

Answer 1

The correct option is A 110${}^{\circ }$, 40${}^{\circ }$ and 30${}^{\circ }$



$\angle HOP$ + 70${}^{\circ }$ = 180${}^{\circ }$ [linear pair]
$\Rightarrow \angle HOP$ = 180${}^{\circ }$ − 70${}^{\circ }$
= 110°
$\because$ Opposite angles of a parallelogram are equal
$\therefore$ x = $\angle HOP$ = 110${}^{\circ }$

$\angle EHO$ + $\angle HEP$ = 180${}^{\circ }$
[Sum of adjacent 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${}^{\circ }$[alternate angles]

$\therefore$ x${}^{\circ }$ = 110${}^{\circ }$
y${}^{\circ }$ = 40${}^{\circ }$
z${}^{\circ }$ = 30${}^{\circ }$