Question

What is the value of z°? Explain how you arrived at that number.

Answer 1

The inscribed angle theorem tells us that

$m\angle COA=2x^\circ\implies x^\circ=53^\circ$

Chord COR passes through the circle's center, so the line segment CR coincides with the circle's diameter. The line containing the line segment RL appears to be tangent to the circle. Taken together, it follows that CR and RL are perpendicular to one another, which means $x^\circ$ and $z^\circ$ are complementary angles. So

$x^\circ+z^\circ=90^\circ\implies z^\circ=37^\circ$