First use the equation 1/2(x+y) to find the missing and third angle that is not labeled for the triangles.
1/2(x+y) 1/2(108+40) 1/2(148) 74
So 74 is the measure of the third angle in the triangle. Next find the measure of w.
W is an inscribed angle that intercepts an arc that has the measure of 108 degrees. Inscribed angles are worth half of the measure of the value of the arc which it intercepts.
108/2=w 54=w
Next use the triangle angle sum theorem to grind the value of z. Set it all up to 180 degrees.
