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Question
In the given figure, AC ⊥ CE and ∠A : ∠B : ∠C = 3 : 2 : 1, find the value of ∠ECD.
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Solution
In the given figure, AC ⊥ CE and ∠A : ∠B:∠C = 3:2:1. We need to find the value of ∠ECD
Since,
∠A : ∠B:∠C = 3:2:1
Let,
∠A = 3x
∠B = 2x
∠C = x
Applying the angle sum property of the triangle, in ΔABC, we get,
∠A + ∠B + ∠C = 180°
3x + 2x + x = 180°
6x = 180°
`x = (180°)/6 `
`x = 30°`
Thus,
∠A = 3x = 3(30°) = 90°
∠B = 2x = 2 (30°) = 60°
∠C = x = 30°
Further, BCD is a straight line. So, applying the property, “the angles forming a linear pair are supplementary”, we get,
∠C + ∠ACE + ∠ECD = 180°
∠EDC = 30° + 90° = 180°
∠ECD + 120° = 180°
∠ECD = 180° - 120°
∠ECD = 60°
Therefore, ∠ECD = 60°.
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