Question

Find $x$ in terms of $y$ and $z$ if $\overline{AB}$ and $\overline{CD}$ are parallel as shown in the above figure.

• A. $y+z$
• B. $2y+z$
• C. $2y-z$
• D. $180-y-z$
• E. $180+y-z$

Answer 1

The correct option is A $y+z$

We know that interior angle sum theorem to pentagon $ABECD$. Since line $AD$ is transversal to the parallel lines $AB$ and $CD$, it follows that $\angle BAD$ and $\angle ADC$ are supplementary.

The sum of the two angles $={180}^o$

The measure of $\angle BEC$, interior to polygon $ABECD$ is $(360–x{)}^o$.

The sum of the measure of the interior angle of pentagon $ABECD$ is ${180}^o+(360-x{)}^o+y^o+z^o$.

The interior angle sum theorem applied to pentagon $ABECD$ gives the equation ${180}^o+(360-x{)}^o+y^o+z^o={540}^o$

$\Rightarrow -x^o+y^o+z^o={540}^o-{540}^o$

$\Rightarrow x^o=y^o+z^o$ is the answer.