Question

find m∠jlk.

Explanation:

Step1: Identify the triangle type

Since \( LK = JK \), \(\triangle LJK\) is an isosceles triangle. In an isosceles triangle, the base - angles are equal. So, \(\angle JLK=\angle LJK\).

Step2: Use the triangle - angle sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(m\angle JLK = x\). Then \(x + x+58^{\circ}=180^{\circ}\).
Simplify the equation: \(2x=180^{\circ}- 58^{\circ}\).
\(2x = 122^{\circ}\).
Solve for \(x\): \(x=\frac{122^{\circ}}{2}\).

Answer:

\(51^{\circ}\)