in the diagram of the circle shown below:
• $ \overline { a b } $ and $ \overline { a c } $ are tangent to the circle
• $ m \widehat { b c } = 95 ^ { \circ } $
• $ m \widehat { b d c } = 265 ^ { \circ } $
which statement describes how to calculate the measure of $ m \angle b a c $ ?
$ m \angle b a c $ is a third of the sum of the measures of $ m \widehat { b d c } $ and $ m \widehat { b c } $, or $ 120 ^ { \circ } $.
$ m \angle b a c $ is a fourth of the sum of the measures of $ m \widehat { b d c } $ and $ m \widehat { b c } $, or $ 90 ^ { \circ } $.
$ m \angle b a c $ is a third of the difference of the measures of $ m \widehat { b d c } $ and $ m \widehat { b c } $, or $ 56 ^ { \circ } $.
$ m \angle b a c $ is half of the difference of the measures of $ m \widehat { b d c } $ and $ m \widehat { b c } $, or $ 85 ^ { \circ } $.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the angle formed by two tangents
The measure of an angle formed by two tangents drawn from an external point to a circle is half the difference of the measures of the intercepted arcs. The formula is $m\angle BAC=\frac{1}{2}(m\widehat{BDC}-m\widehat{BC})$.
## Step2: Substitute the given values
Given $m\widehat{BDC} = 265^{\circ}$ and $m\widehat{BC}=95^{\circ}$. Then $m\angle BAC=\frac{1}{2}(265 - 95)$.
$$
\begin{align*}
m\angle BAC&=\frac{1}{2}(170)\
& = 85^{\circ}
\end{align*}
$$

# Answer:
$m\angle BAC$ is half of the difference of the measures of $m\widehat{BDC}$ and $m\widehat{BC}$, or $85^{\circ}$.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the angle formed by two tangents

Step2: Substitute the given values

Answer: