Question

question
in △klm, $overline{kl}congoverline{mk}$ and m∠m = 22°. find m∠k.

Explanation:

Step1: Identify isosceles - triangle

Since $\overline{KL}\cong\overline{MK}$ in $\triangle KLM$, $\triangle KLM$ is an isosceles triangle with base - angles equal. So, $\angle L=\angle M = 22^{\circ}$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. Let $m\angle K=x$. Then $x + m\angle L+m\angle M=180^{\circ}$.
Substitute $m\angle L = 22^{\circ}$ and $m\angle M = 22^{\circ}$ into the equation: $x+22^{\circ}+22^{\circ}=180^{\circ}$.

Step3: Solve for $m\angle K$

$x=180^{\circ}-(22^{\circ}+22^{\circ})=180^{\circ}-44^{\circ}=136^{\circ}$.

Answer:

$136^{\circ}$