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An isosceles trapezoid has both legs of equal length. LK = MN

Lower base angles are equal. ∠ K = ∠ N
Upper base angles are equal. ∠ L = ∠ M
Opposite angles are supplementary. ∠ K + ∠ M = 180°  

If you picture the top LM = 3 moving down to the bottom base KN, it makes two equal lengths on either side. 13 - 3 = 10
KH = 5
HN = 8

You can use the Pythagorean theorem to find the altitude (LH). 
8² + (LH)² = (√89)²
64 + (LH)² = 89
(LH)² = 89 - 64
(LH)² = 25
LH = 5

Soh Cah Toa

Tan(LKN) = 5/5
inverse trig function

∠LKN = 45°

Tangent is a trigonometric function. The measure of the ∠LKN is 45°.

What is Tangent (Tanθ)?

Tangent is a trigonometric function which is equal to the quotient of the perpendicular side divided by the base. it is given as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

In the ΔLHN,

[tex](LN)^2 = (LH)^2+(HN)^2\\\\(\sqrt{89})^2 = (LH)^2+(8)^2\\\\89 = (LH)^2+64\\\\25=(LH)^2\\\\LH = 5[/tex]

Now, in ΔLHK, the side LH and KH are known, therefore, the measure of ∠LKN using the tangent function can be written as,

[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\\\\tan(\angle LKH) = \dfrac{LH}{KH}\\\\tan(\angle LKH) = \dfrac{5}{5}\\\\(\angle LKH) = tan^{-1}(\dfrac55)\\\\(\angle LKH) = 45^o[/tex]

Hence, the measure of the ∠LKN is 45°.

Learn more about Tangent (Tanθ):

https://brainly.com/question/10623976

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