Question

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

Explanation:

Step1: Recall the sum of interior angles of a quadrilateral

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

Step2: Use the property of a kite

In kite \(KLMN\), \(\angle L=\angle N = 106^{\circ}\), \(\angle K = 99^{\circ}\). Let \(\angle LMN=x\).
We know that \(\angle L+\angle N+\angle K+\angle LMN = 360^{\circ}\).
Substitute the values: \(106^{\circ}+106^{\circ}+99^{\circ}+x=360^{\circ}\).

Step3: Solve for \(x\)

First, calculate \(106 + 106+99=311\). Then \(x=360 - 311\).
\(x = 49^{\circ}\)

Answer:

\(49^{\circ}\) (the first option)