pls help this is the 3rd time i've put up this question...Given: KLMN is a trapezoid, KL = MNLN = 89 , LH- altitude LM = 3, KN = 13. Find: m∠LKN

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°