(a(i))[2]
Show that $x^2 + 12x - 195 = 0$.
(a(ii))[3]
Calculate $AB$, giving your answer correct to $1$ decimal place.
(a(iii))[2]
Since $AD$ is $0.8\text{ cm}$ longer than $BC$, and the perimeter of the trapezium is $38.0\text{ cm}$, calculate $AD$.
(b(i))[2]
A different trapezium, $LMNO$, has $LM$ parallel to $ON$. The reflex angle $LMN = 252^\circ$. Calculate $\angle MNO$.
(b(ii))[3]
The angle ratios inside the trapezium are $\angle LON : \angle LMN = 1 : 2$ and $\angle OLM : \angle MNO = 1 : k$. Find $k$, giving your answer as a fraction in simplest form.