Euclidean Geometry Circles

Question

In the diagram below, XY is a chord of the circle that goes through X, Y and Z. WZ is a tangent to the circle. XZ = YZ XZW = x-30 degrees XZY = 4x

I want to calculate the value of x in order to move on to the next steps. Any advice or tips on where to start?

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Answer 1

Just use the simple angle and chord rules.

Answer 2

$\angle XZW = \angle XYZ = \angle YXZ$. From triangle $XYZ$, $$2(x-30^\circ)+4x = 180^\circ$$ and hence $6x = 240^\circ$ and $x = 40^\circ$