Question

Kite K L M N is shown. The lengths of sides L M and M N are congruent. The lengths of L K and K N are congruent. Angle K is 99 degrees and angle N is 106 degrees. What is the measure of LMN in kite KLMN? 49° 99° 106° 155°

Answer 1

∠LMN = 49°

Explanation:

Given that

∠LKN = 99°

∠MNK = 106°.

Because, the lengths of LK and KN are congruent.

LK=KN because congruent lines are equal

Hence, ∠MNK=∠MLK = 106°

Adding all angles together, we have

∠MNK + ∠MLK + ∠LKN + ∠LMN = 360°

By substituton;

We have

106° + 106° + 99° + ∠LMN = 360°

311° + ∠LMN = 360°

Collect like terms

∠LMN = 360° - 311°

∠LMN = 49°

Answer 2

`\angle \ LMN=49\textdegree`

Explanation:

The diagonals of kite KLMN meet at 90°

Since, LK and KN are congruent,
`\angle KLM` and
`\angle KNM` form a set of opposite congruent angles. Congruent angles are equal.

All interior angles of a kite add up to 180°, therefore:-

`\angle LMN=360\textdegree - 2*106\textdegree-99\textdegree\\=49\textdegree`