Question

$\overleftrightarrow{st}$ is tangent to the circle at $u$. find the measure of $\angle tuv$.
write your answer as a whole number or a decimal.
$m\angle tuv = \square^\circ$

Explanation:

Step1: Find the measure of the minor arc UV

The total circumference of a circle corresponds to \(360^\circ\). The major arc UV is given as \(236^\circ\), so the minor arc UV is \(360^\circ - 236^\circ = 124^\circ\).

Step2: Use the tangent-chord angle theorem

The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc. So, \(\angle TUV\) is half of the measure of the minor arc UV.

$$ m\angle TUV = \frac{1}{2} \times 124^\circ = 62^\circ $$

Answer:

\(62\)