The pie chart below shows the percentage break-up of the costs incurred in printing a magazine. What is the angle of the sector representing the paper cost?
Show Hint
Use the fact that 100% of the pie equals 360 degrees, so each 1% equals 3.6 degrees.
The chart's percentages must add up to $100\%$, and the full circle is $360^\circ$, so check each option against that link.
10 degrees: this would be the answer only if someone wrongly assumed 1% equals 1 degree, but a full circle is 360 degrees for 100%, not 100 degrees, so this option is wrong.
36 degrees: using $1\% = 3.6^\circ$, paper cost's $10\%$ share works out to $10 \times 3.6 = 36^\circ$, matching this option exactly.
23.5 degrees: this number does not correspond to $10\%$ of $360^\circ$ under any simple rounding, so it can be ruled out.
45 degrees: this would be the angle for a $12.5\%$ share, not the $10\%$ share shown for paper cost, so this option is wrong.
Only the second option lines up with the correct conversion of $10\%$ into degrees.
Let's summarize:
Remember that $100\% = 360^\circ$, so $1\% = 3.6^\circ$.
Multiply the given percentage share by $3.6$ to get its angle.
Cross check the remaining options by seeing what percentage they would represent instead.
