Answer: The correct option is (C) 6.
Step-by-step explanation: We are given a triangle ABC in the figure, in which
[tex]m\angle A=m\angle C=63^\circ,~~~AB=3x~\textup{units}~~\textup{and}~~BC=(4x-2)~\textup{units}.[/tex]
We are given to find the length of side AB.
In ΔABC, we have
[tex]m\angle A=m\angle C.[/tex]
We know that in a triangle,
if two angles have equal measures, then the sides opposite to them are equal in length.
So, we must have
[tex]BC=AB\\\\\Rightarrow 4x-2=3x\\\\\Rightarrow 4x-3x=2\\\\\Rightarrow x=2.[/tex]
Therefore, the length of AB will be
[tex]AB=3x=3\times 2=6.[/tex]
Thus, the length of side AB is 6 units.
Option (C) is CORRECT.
