Question

question 10 of 10
in the diagram below, $overline{xy}$ and $overline{yz}$ are tangent to $odot o$. which expression gives the measure of $angle xyz$?
a. $245^{circ}+115^{circ}$
b. $\frac{1}{2}(245^{circ}-115^{circ})$
c. $245^{circ}-115^{circ}$
d. $\frac{1}{2}(245^{circ}+115^{circ})$

Explanation:

Step1: Recall tangent - arc relationship

The measure of an angle formed by two tangents to a circle is half the difference of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The larger intercepted arc is $245^{\circ}$ and the smaller intercepted arc is $115^{\circ}$.

Step3: Apply the formula

The measure of $\angle XYZ=\frac{1}{2}(\text{major arc}-\text{minor arc})=\frac{1}{2}(245^{\circ}-115^{\circ})$.

Answer:

B. $\frac{1}{2}(245^{\circ}- 115^{\circ})$