Question

ABCDE is a pentagon in which AB is parallel to ED. If $\angle B={142}^{\circ }$, $\angle C=3x^{\circ }$ and $\angle D=2x^{\circ }.$ Calculate $x$.

• A. $43.6$
• B. $50.00$
• C. $42.8$
• D. $56.34$

Answer 1

The correct option is A $43.6$

ABCDE is a pentagon in which AB is parallel to ED and $\angle B={142}^o,\angle C=3x^{o}and\angle D=2x^o$
So,
$\angle A+\angle E={180}^o$ ...(Sum of interior angle on the same side of a transversal is supplementary.)
Now,
$\angle B+\angle C+\angle D+\angle A+\angle E={180}^o(n-2)$
$=>{142}^o+3x^o+2x^o+{180}^o={180}^o(5-2)$
$=>5x^o={540}^o-{180}^o-{142}^o$
$=>x^o=\frac{{218}^o}{5}={43.6}^o$
$x=43.6$