Within the diagram, $ABCD$ forms a parallelogram. $P$ and $Q$ lie on $AB$ and $BC$ respectively, with $PB = BQ$ and $DPQ = 90^\circ$. $BPQ = a^\circ$.
(a(i))[1]
Find, in terms of $a$, an expression for $\angle PBQ$.
(a(ii))[1]
Find, in terms of $a$, an expression for $\angle APD$.
(a(iii))[1]
Find, in terms of $a$, an expression for $\angle DAP$.
(a(iv))[1]
Find, in terms of $a$, an expression for $\angle ADP$.
(b(i))[1]
Given that $AB = 8\text{ cm}$ and $AD = 4.7\text{ cm}$, find $PB$.
(b(ii))[2]
Given also that $\angle DAB = 54^\circ$, calculate the area of the parallelogram.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “So the expression is $180-2a$, or equally $2(90-a)$.” …