Sum of angles in cyclic pentagon My son got stuck on the March 9th puzzle from Corbett's conundrums (a website of maths questions designed for school children):



Unfortunately, I don't know how to help him solve this, can anyone here help?

We've found that opposite angles in a cyclic quadrilateral add up to 180 degrees, and this lets you write down various equations, but we just end up going round and round without progress.

My feeling is that we have not properly understood the question as it feels like we can move the north-east vertex around the circle and change the value of x without changing the value of y, so I don't see how there could be a specific answer for x+y.

Can anyone propose either a solution, or perhaps suggest the most likely missing piece of information that would make the problem solvable?
Yes, you can't get a numeric value for $x+y$ on the information given.

If you have the value of angle $a$ in the diagram below, you can infer the value of $x+y$ from that via $z=180-y$ and $w=180-x$.
To get answer use property of circle ,
The measure of an inscribed angle is equal to half the measure of the intercepted arc
As per above circle ,
Answer is 
X+Y=180°+a