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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° |
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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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