# Euclidean Geometry Circles

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?

enter image description here

$\angle XZW = \angle XYZ = \angle YXZ$. From triangle $XYZ$, $$2(x-30^\circ)+4x = 180^\circ$$ and hence $6x = 240^\circ$ and $x = 40^\circ$
• Expand the equation $2(x-30^\circ)+4x = 180^\circ$ to get $2x - 60^\circ + 4x = 180^\circ$. – user348749 Sep 15 '16 at 9:37