Question

1. what is m∠k?

Explanation:

Step1: Recall sum of angles in a quadrilateral

The sum of the interior - angles of a quadrilateral is $360^{\circ}$.

Step2: Set up the equation

Let $m\angle K=x$. We know that the other angles are $m\angle J = 28^{\circ}$, $m\angle L=63^{\circ}$, and assume the fourth - angle is $y$. So, $x + 28^{\circ}+63^{\circ}+y=360^{\circ}$.

Step3: Analyze the given information

We can also use the fact that if we consider the relationship between the two quadrilaterals (not necessary in this case as we can directly calculate). Just using the angle - sum property of a quadrilateral:
\[x=360^{\circ}-(28^{\circ}+63^{\circ}+y)\]
Since we are dealing with a single quadrilateral $JKLM$, and we know that the sum of the interior angles of a quadrilateral $A + B + C+D = 360^{\circ}$. Here, $A = m\angle J=28^{\circ}$, $B = m\angle K$, $C = m\angle L = 63^{\circ}$, and let the fourth - angle be $D$.
\[m\angle K=360^{\circ}-(28^{\circ}+63^{\circ}+149^{\circ})\]
\[m\angle K=360^{\circ}-(240^{\circ})\]
\[m\angle K = 120^{\circ}\]

Answer:

$120^{\circ}$