Answer: The correct option is (D) 18.
Step-by-step explanation: We are given to find the length of side AB from the figure shown.
From the figure, we see that
ABC is a triangle, in which m∠A = m∠C = 65°, AB = 6x and BC = 3x+9.
Now, since the measures of angles A and C are equal, so the triangle ABC is an isosceles one with sides opposite to the equal angles equal.
That is,
[tex]BC=AB\\\\\Rightarrow 3x+9=6x\\\\\Rightarrow 6x-3x=9\\\\\Rightarrow 3x=9\\\\\Rightarrow x=\dfrac{9}{3}\\\\\Rightarrow x=3.[/tex]
Therefore, we get
[tex]AB=6x=6\times 3=18.[/tex]
Thus, option (D) is CORRECT.
