Question

find m∠lmk. answer attempt 1 out of 2 m∠lmk = ° submit answer

Explanation:

Step1: Recall isosceles - triangle property

In $\triangle LMK$, since $LK = MK$ (indicated by the equal - side markings), $\angle MLK=\angle K$. Let $\angle MLK = \angle K=x$.

Step2: Use angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So in $\triangle LMK$, we have $\angle LMK + \angle MLK+\angle K=180^{\circ}$. We know that $\angle MLK = 131^{\circ}$, and $\angle MLK+\angle K = 180^{\circ}-\angle LMK$. Also, $\angle MLK=\angle K$. So $131^{\circ}+x + x=180^{\circ}$.

Step3: Solve the equation for $x$

Combining like terms, we get $131^{\circ}+2x = 180^{\circ}$. Subtract $131^{\circ}$ from both sides: $2x=180^{\circ}-131^{\circ}=49^{\circ}$. Then divide both sides by 2: $x = 24.5^{\circ}$.

Answer:

$24.5$