In equilateral ΔABC, D and E are points on the sides AB and AC, respectively, such that AD = CE. BE and CD intersect at F. The measure (in degrees) of ∠CFB is:
120°
Given:
D and E are points located on the sides AB and AC respectively.
AD = CE
BE and CD intersect at F.
Concept Used:
Concept of triangle congruence,
The exterior angle is always equal to the sum of the opposite interior angles.
Calculation:
ΔCBE ≅ ΔACD [SAS Congruence]
Thus, all three angles of these two triangles are equal,
Let ∠EBC be θ, then ∠ACD is also θ.
Now,
∠BEC = 180° - (60° + θ)
⇒ 120° - θ
Now, in ΔECF
The exterior angle ∠CFB = (120° - θ) + θ
⇒ 120°
∴ ∠CFB is 120° .
Important Questions from Properties of Triangles
What is the perimeter of the triangle ?
Consider the following statements :
1. ABC is right angled triangle
2. The angles of the triangle are in AP
Which of the statements given above is/are correct ?
What is the nature of the triangle ?
If c = 8, what is the area of the triangle ?
What is the value of n ?
