question 3 of 10
in the diagram below, $ \overline { x y } $ and $ \overline { y z } $ are tangent to $ \odot o $. what is the measure of $ \angle x y z $ ?
a. $ 102 ^ { \circ } $
b. $ 51 ^ { \circ } $
c. $ 47 ^ { \circ } $
d. $ 64 ^ { \circ } $

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Accepted Answer

# Explanation:
## Step1: Recall the formula for the measure of an angle formed by two tangents
The measure of an angle formed by two tangents outside a circle is given by $\angle XYZ=\frac{1}{2}(m\overset{\frown}{major\ arc}-m\overset{\frown}{minor\ arc})$.

## Step2: Identify the measures of the arcs
The measure of the major arc is $231^{\circ}$ and the measure of the minor arc is $129^{\circ}$ (since $360 - 231=129$).

## Step3: Substitute the values into the formula
$$
\begin{align*}
\angle XYZ&=\frac{1}{2}(231 - 129)\
&=\frac{1}{2}(102)\
& = 51^{\circ}
\end{align*}
$$

# Answer:
B. $51^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the measure of an angle formed by two tangents

Step2: Identify the measures of the arcs

Step3: Substitute the values into the formula

Answer: