A, B, C and D are points on the circumference of a circle, centre O - Edexcel - GCSE Maths - Question 21 - 2022 - Paper 2

Next, we can find angle DAB which is an inscribed angle that subtends the same arc AD. Thus:

$\angle DAB = \frac{1}{2} \times \angle AOD = \frac{1}{2} \times 228° = 114°$

This follows from the Inscribed Angle Theorem, which states that the angle at the circumference is half that of the angle at the center.

Now, we look at triangle CDE. We know from the linear pair that:

$\angle ADE + \angle CDE = 180°$

Given that angle ADE is 16° from the question, we have:

$16° + \angle CDE = 180°$

Thus, we can solve for angle CDE:

$\angle CDE = 180° - 16° = 164°$