Question

vw is tangent to the circle at w. find the measure of ∠uvw. write your answer as a whole number or a decimal. m∠uvw = °

Explanation:

Step1: Find the measure of the major arc

The sum of the measures of the arcs in a circle is \(360^{\circ}\). Given one arc is \(178^{\circ}\) and another is \(85^{\circ}\), the major arc \( \overset{\frown}{TW}\) is \(360^{\circ}-85^{\circ}=275^{\circ}\) (but we use the formula for the angle formed by a secant and a tangent: \(\angle UVW=\frac{1}{2}(\text{major arc}-\text{minor arc})\). The major arc corresponding to the angle formed by secant \(VT\) and tangent \(VW\) is \(178^{\circ}\), and the minor arc is \(85^{\circ}\)

Step2: Apply the angle - secant - tangent formula

The formula for the angle formed by a secant and a tangent is \(\angle UVW=\frac{1}{2}(\text{measure of the intercepted major arc}-\text{measure of the intercepted minor arc})\)

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Answer:

\(46.5\)