In the given figure, $\triangle ABC$ is an equilateral triangle whose side BC has been produced in both the directions to D and E respectively. Prove that $\angle ACD =\angle ABE$.
Use the given figure to express: (i) $a$ in terms of $b$ and $f$; (ii) $e$ in terms of $f$ and $g$; (iii) $d$ in terms of $a$ and $e$; (iv) $c$ in terms of $e$ and $g$.
Answer
(i) $a=f-b$, (ii) $e=g-f$, (iii) $d=a+e$, (iv) $c=e+\left(180^{\circ}-g\right)$