In circle J, the measure of minor arc $HK$ is given as $58^{\circ}$. We need to find the measure of angle $HLK$.

1. Problem Description

In circle J, the measure of minor arc $HK$ is given as $58^{\circ}$. We need to find the measure of angle $HLK$.

2. Solution Steps

The angle $HLK$ is an inscribed angle that intercepts the arc $HK$. The inscribed angle theorem states that the measure of an inscribed angle is half the measure of its intercepted arc.

In this case, $\angle HLK$ intercepts the arc $HK$. Therefore,

$m\angle HLK = \frac{1}{2} \times m\stackrel{\frown}{HK}$

We are given that $m\stackrel{\frown}{HK} = 58^{\circ}$.

Substituting this value into the formula, we get:

$m\angle HLK = \frac{1}{2} \times 58^{\circ}$

$m\angle HLK = 29^{\circ}$

3. Final Answer

The measure of angle $HLK$ is $29^{\circ}$.