Question

$\overrightarrow{fe}$ is tangent to the circle at e. $\overrightarrow{fg}$ is tangent to the circle at g. find the measure of $\angle efg$.
write your answer as a whole number or a decimal.
$m\angle efg = \square ^\circ$

Explanation:

Step1: Find the measure of the major arc

The measure of a full - circle is \(360^{\circ}\). Given the measure of the minor arc \(EG\) is \(98^{\circ}\), then the measure of the major arc \(EG\) is \(360^{\circ}-98^{\circ}=262^{\circ}\).

Step2: Use the formula for the angle formed by two tangents

The formula for the measure of an angle formed by two tangents is \(\angle EFG=\frac{1}{2}(\text{major arc}-\text{minor arc})\).
Substitute the values of the major arc (\(262^{\circ}\)) and the minor arc (\(98^{\circ}\)) into the formula: \(\angle EFG=\frac{1}{2}(262 - 98)\).
First, calculate the value inside the parentheses: \(262-98 = 164\).
Then, multiply by \(\frac{1}{2}\): \(\frac{1}{2}\times164=82\).

Answer:

\(82\)