Question : Study the given pie chart and answer the question that follows.
The pie chart shows the number of female students in six different colleges P, Q, R, S, T, and U, as percentages of the total number of female students in all these six colleges.
What is the sum of the measures of the central angles of the sectors corresponding to the number of females in colleges Q and U taken together?
Option 1: 96°
Option 2: 108°
Option 3: 97.2°
Option 4: 86.4°
Correct Answer: 97.2°
Solution :
The measure of the central angle is equal to $\frac{\text{Percent share of the corresponding sector}}{100}\times360$.
Measure of central angle for Q = $\frac{15}{100}\times360$ = 54$^\circ$
Measure of central angle for U = $\frac{12}{100}\times360$ = 43.2$^\circ$
$\therefore$ The sum of the measures of the central angles of the sectors corresponding to the number of girls in colleges Q and U, taken together is = 54$^\circ$ + 43.2$^\circ$ = 97.2$^\circ$
Hence, the correct answer is 97.2$^\circ$.
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