Question

It is given that, AB || DE. Find the value of y, if $\angle$ABC= ${110}^{\circ }$ and $\angle$CDE= ${100}^{\circ }$.

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A

${30}^{\circ }$

Draw a line PQ passing though C and parallel to AB and DE, as shown in the figure below:

$\angle$ABC = ${110}^{\circ }$ (given)

$\angle$PCB = ${70}^{\circ }$ (co-interior angles as PQ || AB)

$\angle$CDE = ${100}^{\circ }$ (given)

$\angle$QCD = ${80}^{\circ }$ (co-interior angles as PQ || DE)

Since PQ is a straight line,
y = 180${}^{\circ }$ - (70${}^{\circ }$ + 80${}^{\circ }$)
= ${30}^{\circ }$