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The difference between two angles measuring $36 °$ and $24 ° 28 ′ 30 ′ ′$ from the following choices is

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11 ° 31' 30''

11 ° 30' 30''

21 ° 31' 30''

12 ° 30' 30''

answer is A.

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Detailed Solution

It is given two angles measuring

36 °

and

24 ° 28 ′ 30 ′ ′

.
To find the difference between the angles.
Suppose the angles be

∠ A, ∠ B

.
Write

∠ A

expressing it in terms of degrees, minutes and seconds.

∠ A = 36 ° 0' 0''

∠ B = 24 ° 28' 30''

Split

∠ A

using

36 ° = 35 ° 59' 60 "

, so angle becomes,

36 ° = 35 ° 59' 60''

The difference of the angle is given by,

∠ A − ∠ B = 35 ° 59' 60'' − 24 ° 28' 30''

= 11 ° 31' 30''

Hence the difference is

11 ° 31' 30''

.
Hence option 1) is correct.

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