The measure of an angle formed by two tangents to a circle is half the difference o...
Check the final answer first, then review the worked steps.
Problem
The measure of an angle formed by two tangents to a circle is half the difference of the intercepted arcs.
Step-by-step solution
The angle $\angle XYZ$ is formed by two tangents. The intercepted arcs are $231^\circ$ and $129^\circ$. The measure of the angle is $\frac{1}{2}(231^\circ - 129^\circ) = \frac{1}{2}(102^\circ) = 51^\circ$.
Answer
$51^\circ$