The angle m∠LKN is equal to 45 degrees.
To understand more, check below explanation.
Trapezoid :
It is given that,
KL = MN, LM =3 , KN = 13 and LN [tex]=\sqrt{89}[/tex]
So that, HN = 13 - (13-3)/2 = 13 - 5 = 8
[tex]LN = \sqrt{(HN)^{2}+(LH)^{2} }\\\\\sqrt{89} = \sqrt{(8)^{2}+(LH)^{2} }\\\\89=64+(LH)^{2} \\\\LH=\sqrt{25}=5[/tex]
Since, HN = 8. So that, HK = 13 - 8 = 5
In a triangle, if two sides are equal. Then, opposite angle of both sides are also equal.
In triangle LKH, LH = HK = 5 and [tex]\angle H=90[/tex]
So that, m∠LKN = 90/2 = 45 degree.
Hence, the angle m∠LKN is equal to 45 degrees.
Learn more about the trapezoid here:
https://brainly.com/question/1463152
