Question

what is the measure of ∠lmn in kite klmn? 49° 99° 106° 155°

Explanation:

Step1: Recall the property of a kite

The sum of the interior angles of a quadrilateral is $360^{\circ}$. In a kite, there are two pairs of adjacent - congruent sides. Let $\angle LMN = x$.

Step2: Set up the angle - sum equation

We know that $\angle K = 99^{\circ}$, $\angle N=106^{\circ}$, and the sum of the interior angles of quadrilateral $KLMN$ is $360^{\circ}$. So, $x + 99^{\circ}+106^{\circ}+\angle L=360^{\circ}$. Also, in a kite, the non - vertex angles between the non - congruent sides are equal. Let's assume the kite has the property that we can use the angle - sum formula directly.
\[x+99^{\circ}+106^{\circ}+\angle L = 360^{\circ}\]
Since the sum of the interior angles of a quadrilateral is $360^{\circ}$, we have:
\[x=360^{\circ}-(99^{\circ} + 106^{\circ})\]
\[x = 360^{\circ}-205^{\circ}\]
\[x = 155^{\circ}\]

Answer:

$155^{\circ}$