Question

11. Find the magnitude of an angle, which is
(1) 2/3 of its supplement.
(ii)1/4
of its complement.
​

Answer 1

Answer:

I) The angle is 72 degree.

II) The angle is 18 degree.

Step-by-step explanation:

I) Let the angle be x degree.

Therefore it's supplement = 180 - x degree.

Also it is 2/3 of its supplement,

Therefore by the problem,

x = 2/3(180 - x)

=> x = 120 - 2x/3

=> x + 2x/3 = 120

=> 5x/3 = 120

=>5x = 120*3

=> x = 24*3

=> x = 72

Therefore the angle is 72 degree.

II) Let the angle be x degree.

Therefore it's complement = 90 - x degree

The angle is also 1/4 of its complement.

Therefore by the problem,

x = 1/4(90 - x)

=> x = 45/2 - x/4

=> x + x/4 = 45/2

=> 5x/4 = 45/2

=>5x/2 = 45

=> x = 45*2/5

=> x = 18

Therefore the angle is 18 degree.

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