Multiple choice

A poll of 200 registered voters was taken before the election for the post of mayor . All 200 voters indicated which 1 of the 4 candidates they would vote for. The results of the poll are given in the table below. Candidate Number of voters Blackcloud 50 Lue 80 Gomez 40 Whitney 30 Find the measure of the central angle of the sector for Gomez if the information in the table were converted into a pie chart.

  1. $\displaystyle { 54 }^{ \circ }$
  2. $\displaystyle { 72 }^{ \circ }$
  3. $\displaystyle { 90 }^{ \circ }$
  4. $\displaystyle { 108 }^{ \circ }$
  5. $\displaystyle { 144 }^{ \circ }$
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B Correct answer
Explanation

Total voters = 200. Gomez has 40 votes. The fraction of the total is 40/200 = 1/5. The central angle is 1/5 * 360 degrees = 72 degrees.

AI explanation

The formula for the central angle of a sector in a pie chart is (Category Value / Total Value) multiplied by 360 degrees. The total number of registered voters is 200, and Gomez has 40 voters. Therefore, the central angle for Gomez is (40 / 200) multiplied by 360 degrees. This simplifies to one-fifth of 360 degrees, which equals 72 degrees.

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