find the measure of arc XZ given tangent angle and major arc
Check the final answer first, then review the worked steps.
Problem
find the measure of arc XZ given tangent angle and major arc
Step-by-step solution
The angle formed by two tangents is $180^\circ - \text{minor arc}$. The major arc is $230^\circ$, so the minor arc is $360^\circ - 230^\circ = 130^\circ$. The angle at $Y$ is $180^\circ - 130^\circ = 50^\circ$. The question asks for the measure of arc $XZ$, which is $130^\circ$.
Answer
130^\circ