Question

given circle ( i ) with chords ( overline{jh},overline{jl},overline{kh} ), and ( overline{kl} ), and ( overleftrightarrow{mjn} ) tangent to ( i ) at point ( j ). find an angle that is congruent to ( angle jlk ).

Explanation:

Step1: Use 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 on the opposite side of the chord.
For tangent \(\overleftrightarrow{MJN}\) and chord \(\overline{JL}\), \(\angle NJL\) is the angle between the tangent and the chord.
\(\angle JLK\) is an inscribed angle.
By the tangent - chord angle theorem, \(\angle NJL\) and \(\angle JLK\) subtend the same arc \(\overset{\frown}{JK}\).

Answer:

\(\angle NJL\)