Question
Download Solution PDF∠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 = ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven,
∠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°
Last updated on May 29, 2025
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