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The diagram shows a kite, ABCD - OCR - GCSE Maths - Question 8 - 2019 - Paper 1
Question 8
The diagram shows a kite, ABCD. AFE and CEF are equilateral triangles. (a) Write down a mathematical name for quadrilateral AFCE. (b) The ratio of angle DAE : angl... show full transcript
Worked Solution & Example Answer:The diagram shows a kite, ABCD - OCR - GCSE Maths - Question 8 - 2019 - Paper 1
Step 1
Step 2
Work out angle x.
Answer
Given the ratio DAE : EAF = 1 : 4, let's denote the angle DAE as . Therefore, angle EAF = . Since angles around point A sum up to 180°, we have:
This simplifies to:
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.