1.

If sum of two angles is 157.5° and difference of the angles is π/8, then what is the value of greater angle ? 1. 67.5° 2. 90° 3. 112.5° 4. 22.5°

Answer» Correct Answer - Option 2 : 90° 

Given:

The Sum of the angles = 157.5°

The difference of the angles = π/8

Concept used: 

Radian measure = (π/180) × degree measure 

Calculation:

Let us take the two angles as 'a' and 'b'

Sum of the angles = a + b = 157.5°       ----(i)

Difference between angles = a - b = π/8

π/8 = (π/180) × degree measure 

⇒ Degree measure = π/8 × (180/π) = 22.5° 

a - b = 22.5°       ----(ii)

Adding the equation (i) and (ii), we get

(a + b) + (a - b) = 157.5° +  22.5° = 180° 

⇒ 2a = 180° 

⇒ a = 90° 

Now, b = 157.5° - 90° = 67.5° 

∴ The value of greater angle is 90° 



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