Question

Two lines AB and DE are parallel to each other. The line CM is parallel to both the lines AB and DE. AE and BD intersect each other at point C. If $\angle$ACB = ${40}^{\circ }$ and $\angle$CED = ${60}^{\circ }$, find the value of $\angle$BCM.

• A. ${60}^{\circ }$
• B. ${80}^{\circ }$
• C. ${120}^{\circ }$
• D. 30${}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ }$

$\angle$CED = ${60}^{\circ }$
$\angle$CED = $\angle$MCE
[$\because$Alternate interior angles]
So, $\angle$MCE = ${60}^{\circ }$

As, $\angle$ACB + $\angle$MCE + $\angle$BCM = ${180}^{\circ }$
$\angle$BCM = ${180}^{\circ }$ - $({60}^{\circ }+{40}^{\circ })$
= ${80}^{\circ }$