To solve for this problem we must know the unique property of triangle which is their sum of angles tends to 180°.
We've been given three angles in figure which are 2x, x + 84 and 3x. Now let's tend their sum to 180°.
[tex]:\implies\rm{2x + x + 84 + 3x = 180}[/tex]
[tex]:\implies\rm{2x + x + 3x + 84 = 180}[/tex]
[tex]:\implies\rm{3x + 3x + 84 = 180}[/tex]
[tex]:\implies\rm{6x + 84 = 180}[/tex]
[tex]:\implies\rm{6x = 180 - 84}[/tex]
[tex]:\implies\rm{6x = 96}[/tex]
[tex]:\implies\rm{x = \frac{96}{6} }[/tex]
[tex]:\implies\rm{x = 16}[/tex]
- Thus the correct option is 16 which is option A).
