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Question
One angle of a triangle is 60°. The other two angles are in the ratio of 5: 7. Find the two angles.
Solution
In Δ ABC,
Let ∠A = 60° and then ∠B: ∠C = 5: 7
But ∠A + ∠B + ∠C = 180° ........(Angles of a triangle)
⇒ 60° + ∠B + ∠C = 180°
⇒ ∠B + ∠C = 180°− 60° = 120°
Let ∠B = 5x and ∠C = 7x
∴ 5x + 7x = 120°
⇒ 12x = 120°
⇒ x =`(120°)/12=10°`
∴ ∠B = 5x = 5 × 10° = 50°
∠C = 7x = 7 × 10° = 70°
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