Question : If the sum and difference of two angles are 135° and $\frac{\pi}{12}$, respectively, then the value of the angles in degree measure is:
Option 1: 70° and 65°
Option 2: 75° and 60°
Option 3: 45° and 90°
Option 4: 80° and 55°
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Correct Answer: 75° and 60°
Solution :
Let the two angles be x and y.
So, x + y = 135°------------------------------(1)
The difference of the two angles is $\frac{\pi}{12}$.
So, x – y = $\frac{\pi}{12}=\frac{180}{12}$ = 15° ---------------------------(2)
Solving equations (1) and (2), we get,
x = 75°
So, y = 135 – 75 = 60°
Hence, the correct answer is 75° and 60°.
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