What is the measure of ∠LMN in kite KLMN?
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we know that
LM=MN
LK=KN
∠MNK=∠MLK
we have
∠MNK=[tex]106\°[/tex]
∠LKN=[tex]99\°[/tex]
so
∠MLK=[tex]106\°[/tex]
The sum of the internal angles in the kite is equal to [tex]360\°[/tex]
∠MNK+∠LKN+∠MLK+∠LMN=[tex]360\°[/tex]
substitute values and solve for ∠LMN
∠LMN=[tex]360\°-106\°-106\°-99\°[/tex]
∠LMN=[tex]49\°[/tex]
therefore
the answer is
∠LMN=[tex]49\°[/tex]
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°.