Question

$\overleftrightarrow{wx}$ is tangent to the circle at $y$. find the measure of $\angle xyz$. write your answer as a whole number or a decimal. $m\angle xyz = \square ^\circ$

Explanation:

Step1: Find the minor arc YZ

The total circumference of a circle is $360^\circ$. The given major arc YZ is $179^\circ$, so calculate the minor arc:
$360^\circ - 179^\circ = 181^\circ$

Step2: Apply tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of its intercepted arc. Here, $\angle XYZ$ intercepts the minor arc YZ:
$\angle XYZ = \frac{1}{2} \times 181^\circ$

Step3: Calculate the final angle

Perform the division:
$\frac{181}{2} = 90.5$

Answer:

$90.5$