Question

What is the measure of ∠LMN in kite KLMN?


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Answer 1

we know that

LM=MN

LK=KN

∠MNK=∠MLK

we have

∠MNK=$106\°$

∠LKN=$99\°$

so

∠MLK=$106\°$

The sum of the internal angles in the kite is equal to $360\°$

∠MNK+∠LKN+∠MLK+∠LMN=$360\°$

substitute values and solve for ∠LMN

∠LMN=$360\°-106\°-106\°-99\°$

∠LMN=$49\°$

therefore

the answer is

∠LMN=$49\°$

Answer 2

Answer:

∠LMN=49°

Step-by-step explanation:

From the figure, it is given that KLMN is a kite and LM=MN and LK=KN, ∠MNK=106° and ∠NKL=99° therefore

If LM=MN, then ∠MNK=∠MLK=106°

Now, ∠MNK+∠LKN+∠MLK+∠LMN=360° (Sum of all the interior angles of kite is 360°)

⇒106°+99°+106°+∠LMN=360°

⇒311°+∠LMN=360°

⇒∠LMN=360°-311°

⇒∠LMN=49°

Thus, the measure of ∠LMN in kite KLMN is 49°.