Question : Study the given histogram that shows the marks obtained by students in an examination and answer the question that follows.
If the total marks obtained by students are represented as a pie chart, then the central angle of the sector representing maks 200 or more but less than 300, is: (correct to the nearest degree)
Option 1: 128o
Option 2: 154o
Option 3: 68o
Option 4: 88o
Correct Answer: 154o
Solution : Central angle of pie chart = $\frac{\text{Given frequency}}{\text{Total frequency}} × 360°$ From the histogram, Number of students who scored marks between 200 and 300 = 45 + 60 = 105 ⇒ Total students = 30 + 45 + 60 + 35 + 40 + 35 = 245 ⇒ Required central angle = $\frac{105}{245} × 360°$ = 154° Hence, the correct answer is 154°.
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Question : The following pie chart shows the percentage expenditure of a country on different heads. The total expenditure is INR 1,680 (in billions). Study the chart and answer the question.
The central angle of the sector representing expenditure on Interest payment is:
Option 1: 90o
Option 2: 72o
Option 3: 54o
Option 4: 108o
If the total marks obtained by students are represented as a pie chart, then the central angle corresponding to marks 250 or more but less than 300 is: (correct to the nearest degree)
Option 1: 188°
Option 2: 88°
Option 3: 68°
Option 4: 128°
Question : In $\triangle \mathrm{ABC}, \angle \mathrm{A}=54^{\circ}$. If I is the incentre of the triangle, then the measure of $\angle \mathrm{BIC}$ is:
Option 1: 68o
Option 2: 54o
Option 3: 148o
Option 4: 117o
Question : The sides $P Q$ and $P R$ of $\triangle P Q R$ are produced to points $S$ and $T$, respectively. The bisectors of $\angle S Q R$ and $\angle T R Q$ meet at $\mathrm{U}$. If $\angle \mathrm{QUR}=59^{\circ}$, then the measure of $\angle \mathrm{P}$ is:
Option 1: 31o
Option 2: 62o
Option 3: 41o
Option 4: 49o
Question : The given pie chart shows the percentage distribution of 450 employees in an organisation. Read the pie chart and answer the question that follows.
What is the central angle of the sector representing the number of employees in department E?
Option 1: $36^\circ$
Option 2: $108^\circ$
Option 3: $72^\circ$
Option 4: $90^\circ$
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