Cyclic quadrilaterals - finding the size of an angle I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question really isn't making much sense to me - I keep coming out with far fetched answers. How do I find the size of the angle W? E being the centre of the circle ABCD. Any help is appreciated!

First, the quadrilateral ABCD is inscribed in the circle, so the opposite angles $\angle B+\angle D=180^\circ$, therefore $\angle B=20^\circ$.

Then there is a theorem (inscribed angle and central angle) which says that $\angle E=2\angle W$, therefore $\boxed{\angle W=40^\circ}$.