Question

In the figure given below, find $x$ if AB || CD.

• A. 45${}^{\circ }$
• B. 55${}^{\circ }$
• C. 60${}^{\circ }$
• D. 70${}^{\circ }$

Answer 1

The correct option is B

55${}^{\circ }$

From the given figure,
$\angle FEC+\angle ECD=180°\angle ECD={180}^{\circ }-{150}^{\circ }={30}^{\circ }$
$\text{(Sum of interior angles on the same}\text{side of the transversal is 180°)}$

$\angle ABC=\angle BCD\left(\text{Alternate interior angles}\right)$

$\Rightarrow x={25}^{\circ }+\angle ECD\Rightarrow x={25}^{\circ }+{30}^{\circ }={55}^{\circ }$