Central Angle

Geometry Level 2

Three friends distributed their property. The ratio of total property, share of first friend and share of second friend is 24 : 7 : 8 24:7:8 . If total property can be seemed as 36 0 ∘ 360^{\circ} in the circle, find the central angle of sector, which represents the share of the third friend.


The answer is 135.

Manish Mayank by Manish Mayank , 20, India

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3 solutions

Vinit Béléy
Sep 27, 2014

Since the total property ratio is 24, Let x represent the value which diminishes the ratio to true values. Therefore total property is 24x ; Share of first friend is 7x ; Share of second friend is 8x.

Since the total property is circular, 24x = 360˚ x = 15˚

Since Share of three friends makes up to 24x: Share of third friend = 24x - 7x - 8x = 9x

Therefore share of third friend is 9x = 9*15˚ = 135˚

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Filly Mare
Jun 16, 2014

If 24 is the full property then 24 equates to 360 degrees on the circle. this means that the first friend gets 360 24 × 7 = 105 \frac{360}{24} \times 7=105 degrees of the circle and 2nd friends gets 360 24 × 8 = 120 \frac{360}{24} \times 8 = 120 degrees. Leaving 135 for the third friend

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From the given ratios we can infer that the ratio of the total property to that of the 3rd friend is 24:9. So 24:9 :: 360:x. x=135.

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