Question

question in △jkl, $overline{lj}congoverline{kl}$ and m∠l = 127°. find m∠k.

Explanation:

Step1: Identify the triangle type

Since $\overline{LJ}\cong\overline{KL}$, $\triangle{JKL}$ is an isosceles triangle. In an isosceles triangle, the base - angles are equal. Let $\angle{J}$ and $\angle{K}$ be the base - angles.

Step2: Use the angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, $m\angle{J}+m\angle{K}+m\angle{L}=180^{\circ}$. Since $m\angle{J} = m\angle{K}$ (base - angles of an isosceles triangle) and $m\angle{L}=127^{\circ}$, we can substitute these values into the equation: $2m\angle{K}+127^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle{K}$

First, subtract $127^{\circ}$ from both sides of the equation: $2m\angle{K}=180^{\circ}- 127^{\circ}=53^{\circ}$. Then divide both sides by 2: $m\angle{K}=\frac{53^{\circ}}{2}=26.5^{\circ}$.

Answer:

$26.5^{\circ}$