The value of ∠BEK will be 120° so option (C) will be correct.
What is congruence?
If two figures are exactly the same in sense of their length side all things then they will be congruent.
If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.
In other meaning, if you can copy a figure then that copy and the original figure will be congruent.
Given figure has two triangles ΔCBE and ΔCKE.
The angle of (6x + 24)° is the same as (10x)° ( given congruency of angle by double line)
So,
6x + 24 = 10x
10x - 6x = 24
4x = 24
x = 6°
So,
Angle ∠BEK
∠BEK = (6x + 24) + (10x)
∠BEK = 6(6) + 24 + 10(6)
∠BEK = 120°.
Hence "The value of ∠BEK will be 120° ".
To learn more about congruent,
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