MCQ
In the given figure, $\text{EAD}\perp\text{BCD}.$ Ray $\text{FAC}$ cuts ray $\text{EAD}$ at a point $A$ such that $\angle\text{EAF}=30^\circ.$ Also, in $\triangle\text{BAC},\angle\text{BAC}=\text{x}^\circ$ and $\angle\text{ABC}=(\text{x}+10).$ Then, value of $x$ is:
  • A
    $20^\circ$
  • $25^\circ$
  • C
    $30^\circ$
  • D
    $35^\circ$

Answer

Correct option: B.
$25^\circ$
$\angle\text{EAF}=\angle\text{CAD} \ ($vertically opposite angles$)$
$\Rightarrow\angle\text{CAD}=30^\circ$
In $\triangle\text{ABD},$ by angle sum property
$\angle\text{A}+\angle\text{B}+\angle\text{D}=180^\circ$
$\Rightarrow(\text{x}+30)^\circ+(\text{x}+10)^\circ+90^\circ=180^\circ$
$\Rightarrow2\text{x}+130^\circ=180^\circ$
$\Rightarrow2\text{x}=50^\circ$
$\Rightarrow\text{x}=25^\circ$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free