Question

given circle l with chords \\( \overline { m j } \\), \\( \overline { m k } \\), and \\( \overline { j k } \\), and \\( \overleftrightarrow { n m o } \\) tangent to l at point m. find an angle that is congruent to \\( \angle j m k \\).

Explanation:

Step1: Recall the tangent - chord angle theorem

The measure of an angle formed by a tangent and a chord is equal to the measure of the inscribed angle that subtends the same arc.
For \(\angle JMK\), the tangent \(NMO\) and chord \(MJ\) form \(\angle JMK\). The inscribed angle that subtends the same arc \(MJ\) is \(\angle JKM\).

Answer:

\(\angle JKM\)