Question

In a triangle abc it is given that angle a: angle b: angle c=3:2:1 and angle acd =90 degree if bc is produced to e the angle ecd equal to

Answer 1

AnswEr :

• ∠ECD is 60° .

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Given :

In ΔABC ,

• ∠A : ∠B : ∠C = 3 : 2 : 1

• CD ⊥ AC

To Find :

• The value of ∠ECD = ?

Solution :

Let us assume that the ,

• ∠ACB = x

• ∠ABC = 2x

• ∠BAC = 3x

According to the angle sum property of the triangle,

➝ ∠ACB + ∠ABC + ∠BAC=180°

➝ x + 2x + 3x = 180

➝ 6x = 180

➝ x = 30°

So, the angles are :

• ∠ACB = x = 30°

• ∠ABC = 2x = 2 × 30 = 60°

• ∠BAC = 3x = 3 × 30 = 90°

Also, we know about the exterior angle property,

which mean's, sum of the two interior angles is equal to the exterior angle !!

➝ ∠ACE = ∠BAC + ∠ABC

➝ ∠ACD + ∠ECD = 90 + 60

➝ 90 + ∠ECD = 90 + 60

➝ ∠ECD = 60 + 90 - 90

➝ ∠ECD = 60°

$\therefore$ The value of angle ECD is 60°.

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You should know :

• Angle sum property of triangle is that the sum of interior angles of a triangle is 180°.

• Sum of angles of a triangle is 180°.

Here, in any ΔABC,

• ∠A + ∠B + ∠C = 180°

• An exterior angle of a triangle is always equal to the sum of the opposite interior angles !!

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Answer 2

Answer:

60

Step-by-step explanation: