In the figure, triangle ABC is a right triangle and m of angle A = 40 degrees. What is the measurement of angle ECD?

Given in a ΔABC ∠A:∠B:∠C=3:2:1 and CD is perpendicular to AC. we have to find the value of ∠ECD.

Let ∠BAC=3x, ∠ABC=2x, ∠ACB=x

By angle sum property of triangle

∠BAC+∠ABC+∠ACB=180°

⇒ 3x+2x+x=180°

⇒ 6x=180° ⇒ x=30°

∴ \angle BAC=3x=3\times 30^{\circ}=90^{\circ}∠BAC=3x=3×30

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=90

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\angle ABC=2x=2\times 30^{\circ}=60^{\circ}∠ABC=2x=2×30

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=60

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\angle ACB=x=30^{\circ}∠ACB=x=30

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By exterior angle property, sum of two interior angle is equal to exterior angle.

i.e ∠ACE=∠BAC+∠ABC

⇒ ∠ACD+∠ECD=90°+60°

⇒ 90°+∠ECD=90°+60° ⇒ ∠ECD=60°