The following pie-chart represents the marks scored by a student. If he obtained $540$ as total marks, answer the following:

In which subject did the student score $120$ marks?

The correct option is C: English

Central angle $=\frac{\text{Observation}}{\text{Total Frequency}}\times {360}^{\circ }$

$\therefore$ Observation (Frequecy of any particular item) $=\frac{\text{Central Angle}}{{360}^{\circ }}\times \text{Total frequency}$

Here, Total frequency $=540$

Marks obtained in Maths $=\frac{{90}^{\circ }}{{360}^{\circ }}\times 540=135$

Marks obtained in English $=\frac{{80}^{\circ }}{{360}^{\circ }}\times 540=120$

Marks obtained in Social $=\frac{{70}^{\circ }}{{360}^{\circ }}\times 540=105$

Marks obtained in Science $=\frac{{65}^{\circ }}{{360}^{\circ }}\times 540=97.5$

Marks obtained in Hindi $=\frac{{55}^{\circ }}{{360}^{\circ }}\times 540=82.5$

So, marks in English is $120.$

OR,

Since $360$ degrees of the pie corresponds to the total marks scored, which is $540.$

The angle made by the sector corresponding to the subject with score $120$ marks

$=\frac{120\times 360}{540}={80}^{\circ }$

From the pie chart, we can see that the sector with central angle ${80}^{\circ }$ corresponds to English.