The diagram displays triangle $EFG$ together with a straight line $HFI$. Line $HFI$ is parallel to $EG$. The labels on the diagram include $\angle EFG = 105^{\circ}$, $\angle EGF = 52^{\circ}$, and angles marked $e^{\circ}$ and $f^{\circ}$.
(a(i))[1]
State the mathematical name for this kind of angle.
(a(ii))[2]
Calculate the value of $e$. Give a geometrical reason for your answer.
(a(iii))[2]
Calculate the value of $f$. Give a geometrical reason for your answer.
(b)[3]
Calculate the interior angle of a regular 7-sided polygon. Give your answer correct to 2 decimal places.
(c)[5]
Calculate the values of $w$, $x$ and $y$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “An obtuse angle” …