In the diagram (not to scale) given above, the value of x is

In the diagram (not to scale) given above, the value of x is

51
$ rac{360}{7}$
$62 rac{6}{7}$
$49 rac{4}{7}$
This question was previously asked in
UPSC CAPF – 2013
The diagram is not provided, but based on typical geometry problems involving angles and the options given, it is highly probable that the diagram shows angles around a central point, or possibly interior angles related by parallel lines, that sum up to a specific value involving 360.
Given the options involving 360/7, a likely scenario is that the angles in the diagram, expressed in terms of x, sum up to 360 degrees.
A common configuration is angles around a point summing to 360 degrees. If the angles were, say, $2x, 3x,$ and $2x$, and they formed the complete angle around a point, then their sum would be 360 degrees.
$2x + 3x + 2x = 360$
$7x = 360$
$x = \frac{360}{7}$ degrees.
This value matches option B.
Angles around a point sum up to 360 degrees. This is a fundamental property in geometry.
Without the actual diagram, we rely on plausible geometric configurations that match the structure of the problem and options. The presence of $\frac{360}{7}$ in the options strongly suggests a setup where the sum of angles is $360$ and the variable appears in a way that results in $7x$. A division of $360$ into parts proportional to 2, 3, and 2 ($2x, 3x, 2x$) fits this perfectly.