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Question

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:

This question was previously asked in
SSC CGL 2020 Tier-II (English) Previous Year Paper (29-Jan-2022)
The correct answer 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° .

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Important Questions from Properties of Triangles

  1. Consider the following statements:

    1. If ABC is a right-angled triangle, right-angled at A, and if sin \(\rm B = \frac 1 3,\)  then cosec C = 3.

    2. If b cos B = c cos C and if the triangle ABC is not right-angled, then ABC must be isosceles.

    Which of the above statements is/are correct?

  2. In a triangle \(ABC\), if \(a\), \(b\) and \(c\) are the lengths of the sides opposite to the angles \(A\), \(B\) and \(C\) respectively, then what is \(\frac{\sin(A-B)}{\sin(A+B)}\) equal to ?
  3. In Δ ABC, ∠B = 90º, AC = 29 cm and BC = 20 cm. Then  \(\frac{{1 - \sin A + \cos A}}{{1 + \sin A + \cos A}}\)  is equal to:

  4. The sides of a triangle are m, n and \(\rm \sqrt{m^2+n^2+mn}\) . What is the sum of the acute angles of the triangle?

  5. Each side of a square subtends an angle of 60° at the tip of a tower of height h meters standing at the centre of the square. If l is the length of each side of the square, then what is h 2equal to?

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