∠A, ∠B and ∠C are three angles of a triangle and ∠A/4 + ∠B/4 + ∠C/5 = 41°, then find the value of ∠A + ∠B = ?

  1. 120°
  2. 100°
  3. 90°
  4. 80°

Answer (Detailed Solution Below)

Option 2 : 100°
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Detailed Solution

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Given,

∠A, ∠B and ∠C are three angles of a triangle.

∠A/4 + ∠B/4 + ∠C/5 = 41°

Formula:

Sum of all three angles of a triangle is 180°.

Calculation:

∠A/4 + ∠B/4 + ∠C/5 = 41°

⇒ (5∠A + 5∠B + 4∠C)/20 = 41°

⇒ (∠A + 4∠A + ∠B + 4∠B + 4∠C)/20 = 41°

⇒ (∠A + ∠B + 4∠A + 4∠B + 4∠C)/20 = 41°

⇒ ∠A + ∠B + 4(∠A + ∠B + ∠C) = 41° × 20

⇒ ∠A + ∠B + 4 × 180° = 820°

⇒ ∠A + ∠B = 820° - 720°

⇒ ∠A + ∠B = 100°

∴ The value of ∠A + ∠B is 100°

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