Using the circle theorem for the intersection of a tangent and a chord:
An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc.
Using the theorem, we can write:
[tex]94^0\text{ = }\frac{1}{2}\text{ }\times x[/tex]
Solving for x:
[tex]\begin{gathered} x\text{ = 2 }\times94 \\ x=188^0 \end{gathered}[/tex]
Similarly, we can write:
[tex]\begin{gathered} \text{z = 2}\times(180-94) \\ z\text{ = 2 }\times86 \\ z=172^0 \end{gathered}[/tex]
Answer:
z = 172 degrees
