Question

The angle that is covered by Category 2 is 72◦. What is the per- centage of Category 2? One of the four categories contains exactly 30% of the received answers. Which? Justify your answers.

Answer 1

The whole pie chart represents 100% of the percentage.

Also, the circle has an angle of 360 degrees.

We can use the rule of three to find the percentage of category 2.

Then:

100%------------------- 360 degrees

x ------------------------- 72 degrees

where x= (100*72) / 360

x = 20 degrees

Hence, the percentage for category 2 is 20%

Now, we need to find which category contains exactly 30%

If we assume that cat 2 + cat 3 represents 50% of the percentage.

Then, the 50% of 360degrees is 180degrees.

Then:

cat 2 + cat 3 = 180

72 + cat 3 = 180

Solve for cat 3

cat 3 = 180 - 72

cat 3 = 108 degrees

So, we can use the rule of three to get the percentage:

100%------------------- 360 degrees

x ------------------------- 108 degrees

where x = (100*108)/360

x = 30%

Hence, category 3 represents 30%.