Question

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

Explanation:

Step1: Recall the property of a kite

In a kite, the sum of interior angles is 360°. Also, there are two pairs of adjacent - congruent sides and the non - vertex angles are equal. Let $\angle LMN = x$.

Step2: Set up the angle - sum equation

We know that $\angle K = 99^{\circ}$, $\angle N=106^{\circ}$, and since $\angle L=\angle N = 106^{\circ}$ (non - vertex angles of a kite are equal). Using the formula $\angle L+\angle M+\angle N+\angle K = 360^{\circ}$, we substitute the known values: $106^{\circ}+x + 106^{\circ}+99^{\circ}=360^{\circ}$.

Step3: Simplify the equation

Combine like terms: $x+(106^{\circ}+106^{\circ}+99^{\circ})=360^{\circ}$, so $x + 311^{\circ}=360^{\circ}$.

Step4: Solve for $x$

Subtract 311° from both sides of the equation: $x=360^{\circ}-311^{\circ}=49^{\circ}$.

Answer:

49°