Question

In the figure above, four line segments meet at a point to form four angles. Calculate the value of $x$.

• A. ${180}^o$
• B. ${240}^o$
• C. ${288}^o$
• D. ${312}^o$

Answer 1

Answer: (C)

${288}^o$

As we know sum of all the angles at a point of intersection $={360}^0$
As per figure, adding all the angles and equating to its sum.
$\frac{x}{2}+\frac{x}{6}+\frac{x}{3}+\frac{x}{4}={360}^0$
$\Rightarrow \frac{24x+8x+16x+12x}{48}={360}^0$
$\Rightarrow 60x={360}^0\times 48$
$\Rightarrow x=\frac{360\times 48}{60}$

$\Rightarrow x={288}^0$
Hence, option C is correct.