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:

Question

Question

This question was previously asked in

SSC CGL Tier 2 Quant Previous Paper 2 (Held On: 3 Feb 2022)

Answer 1

Given:

D and E are points on the sides AB and AC

AD = CE

BE and CD intersect at F

Concept used:

Concept of congruency of the triangle,

The exterior angle is always equal to the sum of the interior opposite angle.

Calculation:

F1 Savita SSC 5-5-22 D3

ΔCBE ≅ ΔACD [SAS congruency]

So, the three angles of these two triangles are the same,

Let ∠EBC be θ from this ∠ACD is also θ

Now,

∠BEC = 180° - (60° + θ)

⇒ 120° - θ

Now, In ΔECF

Exterior angle ∠CFB = (120° - θ) + θ

⇒ 120°

∴ ∠CFB is 120°

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