Question

what is the measure of \\( \angle lmn \\) in kite klmn? \\( 49^{\circ} \\) \\( 99^{\circ} \\) \\( 106^{\circ} \\) \\( 155^{\circ} \\)

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

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

Step2: Use the property of a kite

In kite \(KLMN\), \(\angle L=\angle N\) (not applicable here as we know \(\angle K = 99^{\circ}\), \(\angle N=106^{\circ}\), and let \(\angle LMN=x\)).
We know that \(x + 99^{\circ}+106^{\circ}+\angle MLK=360^{\circ}\). Also, in a kite, two pairs of adjacent sides are equal. Let's use the formula \(x=360^{\circ}-(99^{\circ} + 106^{\circ}+ 99^{\circ})\) (since \(\angle MLK=\angle MKN = 99^{\circ}\) as adjacent sides \(ML = MN\) and \(KL=KN\) give \(\angle MLK=\angle MKN\)).

$$x=360-(99 + 106+99)$$

$$x=360 - 304$$

$$x = 49^{\circ}$$

Answer:

\(49^{\circ}\)