Question
Download Solution PDFIn 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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:
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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