Question

In the figure (not drawn to scale), $EFA$ is a right angled triangle with $EFA={90}^o$ and $FGB$ is and equilateral triangle, find $y-2x$

• A. $2^o$
• B. $8^o$
• C. ${17}^o$
• D. ${20}^o$

Answer 1

The correct option is A $2^o$

In $△FGC,\angle GCF={92}^o$ (Given)
As we know $\angle CGF={60}^o$ (Angle of equilateral triangle)
$\therefore x+{60}^o+{92}^o={180}^o$
$\Rightarrow x={180}^o-{152}^o={28}^o$
Now in $△BCF,\angle CBF={60}^o$
$\angle FCB={180}^o-{92}^o$ (Linear pair)
$\Rightarrow \angle FCB={88}^o$
$\therefore \angle BFC+{88}^o+{60}^o={180}^o$ (Angle sum property)
$\Rightarrow \angle BFC={180}^o-{148}^o={32}^o$
And $\angle AFE={90}^o$
$\Rightarrow y={32}^o={90}^o$

$\Rightarrow y={90}^o-{32}^o={58}^o$
$\Rightarrow y-2x={58}^o-2\times {28}^o={58}^o-{56}^o=2^o$