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 d
egrees and angle N is 106 degrees. What is the measure of LMN in kite KLMN? 49° 99° 106° 155°
2 answers:
Answer:
∠LMN = 49°
Step-by-step 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

Step-by-step explanation:
The diagonals of kite KLMN meet at 90°
Since, LK and KN are congruent,
and
form a set of opposite congruent angles. Congruent angles are equal.
All interior angles of a kite add up to 180°, therefore:-

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