Question

What is the measure of ∠LMN in kite KLMN?


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Answer 1

∠LMN=49°

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°.

Answer 2

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\°`