Multiple choice

Three friends distributed their total property. The ratio of total property, share of first friend and share of second friend is $24 : 7 : 8$. Find the central angle of sector which represents the share of the third friend.

  1. $\displaystyle 72\frac{1^{\circ}}{2}$
  2. $\displaystyle 135^{\circ}$
  3. $\displaystyle 105^{\circ}$
  4. $\displaystyle 67\frac{1^{\circ}}{2}$
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B Correct answer
AI explanation

The total property represents 24 parts, while the first friend receives 7 parts and the second receives 8 parts. This leaves 24 - 7 - 8 = 9 parts for the third friend. Using the method for converting a fractional portion to a central angle, calculate 9/24 of the full circle, which is 360 degrees. This gives an angle of 135 degrees.

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