Question

5 multiple choice 1 point in the figure, \\( \overrightarrow { b a } \\) and \\( \overrightarrow { b c } \\) are tangents of circle \\( o \\). if \\( m \angle b = 55 \\), what is the measure of arc \\( a c \\)? 175 250 62.5 125

Explanation:

Step1: Find the measure of the central angle

The measure of an angle formed by two tangents drawn from an external point is half the difference of the measures of the intercepted arcs. Let the measure of arc \(AC\) be \(x\). The measure of the major arc \(AC\) is \(360 - x\). The formula for the angle formed by two tangents is \(m\angle B=\frac{1}{2}(major\ arc - minor\ arc)\).

Step2: Substitute the values into the formula

We know that \(m\angle B = 55\). Substituting into the formula \(55=\frac{1}{2}((360 - x)-x)\)

First, simplify the right - hand side: \(55=\frac{1}{2}(360 - 2x)\)

Multiply both sides by \(2\): \(110=360 - 2x\)

Then, solve for \(x\):

\(2x=360 - 110\)

\(2x = 250\)

\(x = 125\)

Answer:

\(125\)