Question

in a triangle ABC it is given that angle A ratio angle B ratio angle C is equals to 3 ratio 2 ratio 1 and CD is perpendicular to AC find angle ECD

Answer 1

60 degree will be the answer

Answer 2

Answer:

∠ECD=60°

Step-by-step explanation:

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°

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

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

$\angle ACB=x=30^{\circ}$

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°