Question

In the following figure ABCD is a parallelogram.


Find the measure of x${}^{\circ }$, y${}^{\circ }$ and z${}^{\circ }$?

• A. 100${}^{\circ }$, 80${}^{\circ }$ and 80${}^{\circ }$
• B. 100${}^{\circ }$, 80${}^{\circ }$ and 100${}^{\circ }$
• C. 100${}^{\circ }$, 100${}^{\circ }$ and 80${}^{\circ }$
• D. 120${}^{\circ }$, 80${}^{\circ }$ and 90${}^{\circ }$

Answer 1

The correct option is A 100${}^{\circ }$, 80${}^{\circ }$ and 80${}^{\circ }$

Opposite angles of a parallelogram are equal.
$\Rightarrow y^{\circ }=z^{\circ }$ and $\angle ABC=x^{\circ }={100}^{\circ }$

Now,

$\angle ABC$ + $y^{\circ }$ = 180${}^{\circ }$
[sum of adjacent angles of a parallelogram is 180${}^{\circ }$]

$\Rightarrow y^{\circ }+{100}^{\circ }={180}^{\circ }\Rightarrow y^{\circ }={180}^{\circ }–{100}^{\circ }\Rightarrow y^{\circ }={80}^{\circ }\Rightarrow y^{\circ }=z^{\circ }={80}^{\circ }$

$\therefore$ The measure of $x^{\circ }$, $y^{\circ }$ and $z^{\circ }$ are ${100}^{\circ }$, ${80}^{\circ }$ and ${80}^{\circ }$.