Question

Calculate x. (Similar arrow markings show parallel lines).

• A. ${102}^{\circ }$
• B. ${56}^{\circ }$
• C. ${44}^{\circ }$
• D. ${32}^{\circ }$

Answer 1

The correct option is B ${56}^{\circ }$

Given $DB||FE$ and $AE$ is transversal

$\therefore \angle CBE=\angle FEB$ (Alternate angles)

$\Rightarrow CBE={102}^{\circ }$

Now we know external angle of triangle is equal to sum of interior opposite angles

Applying the same in $△ABC$

$\Rightarrow \angle BAC+\angle ACB=\angle CBE$

$\Rightarrow x+{46}^{\circ }={102}^{\circ }\Rightarrow x={102}^{\circ }-{46}^{\circ }\Rightarrow x={56}^{\circ }$