Question Bank - Mathematics

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In equilateral ?ABC, 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:

A.
120°
B.
135°
C.
125°
D.
105°

Solution:

Given:D and E are points on the sides AB and ACAD = CEBE and CD intersect at FConcept used:Concept of congruency of the triangle,The exterior angle is always equal to the sum of the interior opposite angle. Calculation:?CBE ? ?ACD [SAS congruency]So, the three angles of these two triangles are the same,Let ?EBC be ? from this ?ACD is also ?Now,?BEC = 180° - (60° + ?)? 120° - ?Now, In ?ECFExterior angle ?CFB = (120° - ?) + ?? 120°? ?CFB is 120°

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