Represent the given data about students' favorite games and languages using pie charts. Calculate the central angles for each category.

Step 1: Solve Question 1.
To represent the data by a pie chart, we first calculate the total number of students and then the central angle for each game.
Total number of students $= 28 + 8 + 4 + 4 + 1 = 45$.

The central angle for each game is calculated as:

• Cricket: $\frac{28}{45} \times 360^\circ = 224^\circ$
• Football: $\frac{8}{45} \times 360^\circ = 64^\circ$
• Basketball: $\frac{4}{45} \times 360^\circ = 32^\circ$
• Tennis: $\frac{4}{45} \times 360^\circ = 32^\circ$
• Hockey: $\frac{1}{45} \times 360^\circ = 8^\circ$

To draw the pie chart:

• Draw a circle of any convenient radius.
• Draw a radius.
• Using a protractor, draw sectors with the calculated central angles for each game.
• Label each sector with the corresponding game.

Step 2: Solve Question 2.
To represent the data by a pie chart, we first calculate the total number of students and then the central angle for each language.
Total number of students $= 36 + 20 + 15 + 30 + 31 + 48 = 180$.

The central angle for each language is calculated as:

• Tamil: $\frac{36}{180} \times 360^\circ = 72^\circ$
• Telugu: $\frac{20}{180} \times 360^\circ = 40^\circ$
• Kannad: $\frac{15}{180} \times 360^\circ = 30^\circ$
• Gujrati: $\frac{30}{180} \times 360^\circ = 60^\circ$
• Punjabi: $\frac{31}{180} \times 360^\circ = 62^\circ$
• Bangla: $\frac{48}{180} \times 360^\circ = 96^\circ$

To draw the pie chart:

• Draw a circle of any convenient radius.
• Draw a radius.
• Using a protractor, draw sectors with the calculated central angles for each language.
• Label each sector with the corresponding language.

Step 3: Solve Question 3.
The pie chart shows the following central angles: Summer ($90^\circ$), Winter ($120^\circ$), Rainy ($120^\circ$).
The angle for the unlabeled sector is $360^\circ - (90^\circ + 120^\circ + 120^\circ) = 360^\circ - 330^\circ = 30^\circ$.