Concept:To find the angle of a sector in a pie chart, we calculate the proportion of that category to the total and multiply it by 360 degrees.Explanation:First, let's find the total marks scored in all subjects. The marks are: Telugu (17), English (20), Mathematics (18), Science (16), and Social (19).Total Marks = $17 + 20 + 18 + 16 + 19 = 90$Next, we need to find the angle of the sector representing Mathematics. The marks scored in Mathematics are 18.The proportion of Mathematics marks to the total marks is $\frac{18}{90}$.To convert this proportion into an angle in a pie chart, we multiply it by the total angle of a circle, which is 360 degrees.Angle for Mathematics = $\frac{\text{Marks in Mathematics}}{\text{Total Marks}} \times 360^{\circ}$Angle for Mathematics = $\frac{18}{90} \times 360^{\circ}$Now, let's simplify the calculation:Angle for Mathematics = $\frac{1}{5} \times 360^{\circ}$Angle for Mathematics = $72^{\circ}$So, the angle of the sector representing Mathematics is $72^{\circ}$.Answer:$72^{\circ}$