13.
In a A ABC it is given that
LA: ZB: ZC = 3:2:1 and CD I AC.
Then ZECD =?
(a) 60°
(b) 45°
(c) 75°
(d) 30°
Answers
Answer:
In a △ABC, it is given that
∠A : ∠B :∠C = 3:2:1
It can also be written as
∠A=3x, ∠B=2x and ∠C=x
We know that the sum of all the angles in triangle ABC is 180°.
∠A + ∠B + ∠C = 180°
By substituting the values we get
3x + 2x + x = 180°
By addition
6x=180°
By division
x = 180/6x = 30°
Now by substituting the value of x we get
∠A = 3x = 3 (30° ) = 90°
∠B = 2x = 2 (30° ) = 60°
∠C = x = 30°
We know that in the triangle ABC exterior angle is equal to the sum of two opposite interior angles
So we can write it as
∠ACE = ∠A + ∠B
By substituting the values we get
∠ACE = 90° +60°
By addition
∠ACE = 150°
We know that ∠ACE can be written as ∠ACD+∠ECD
So we can write it as
∠ACE=∠ACD+∠ECD
By substituting the values we get
150° = 90° +∠ECD
It is given that CD⊥ AC so ∠ACDb= 90°
On further calculation
∠ECD = 150° – 90°
By subtraction
∠ECD = 60°
Therefore, ∠ECD=60°.
option a) 60°