The diagram shows a hexagon - Edexcel - GCSE Maths - Question 7 - 2019 - Paper 3

Since the hexagon has one line of symmetry, angles AFE and ABC are equal. Given that angle ABC = 117°, we have:

$\text{Angle AFE} = 117°$.

Next, since angle BCD = 2 × angle CDE, we can express angle BCD as:

$\text{Angle BCD} = 2 \times x \, \text{(where x = angle CDE)}.$

We now know:

$\text{Angle AFE} + \text{Angle ABC} + \text{Angle BCD} + \text{Angle CDE} + \text{Angle EFD} = 720°$ Substituting the known angles:

$117° + 117° + 2x + x + 2x = 720°$ This simplifies to:

$234° + 5x = 720°$.

By subtracting 234° from both sides, we get:

$5x = 486°$.

Now, solve for x:

$x = \frac{486°}{5} = 97.2°$.

Using the value of x to find angle AFE:

Now since angle CDE = 97.2°, we can conclude:

$\text{Angle BCD} = 2 \times 97.2° = 194.4°$

Finally:

$\text{Angle AFE} = 117°$

Therefore, the size of angle AFE is 117°.