The diagram shows a kite, ABCD - OCR - GCSE Maths - Question 8 - 2019 - Paper 1

Given the ratio DAE : EAF = 1 : 4, let's denote the angle DAE as $heta$. Therefore, angle EAF = $4 heta$. Since angles around point A sum up to 180°, we have:

$heta + 4 heta + x = 180°$

This simplifies to:

$5 heta + x = 180°$

To find x, we also need to consider that triangles AFE and CEF are equilateral. Therefore, angles AFE and CEF are each 60°. Thus, angle EAF = angle AFE = 60° implies:

ightarrow heta = 15°$$ Substituting $ heta$ back into the angles at point A: $$5(15°) + x = 180°$$ $$75° + x = 180°$$ $$x = 180° - 75°$$ $$x = 105°$$ Thus, angle x = 105°. You should also note angle DAE = 15° and EAF = 60° on the diagram.