Given: KLMN is a trapezoid, KL = MN, LN=89,
LM=3, KN=13
Find: m ZLKN.
L
M
N
K

45°

Step-by-step explanation:

draw point L' and M' and make line LL' and MM' which perpendicular to KN

so we have rectangle of LMM'L'

KL' = M'N = (13-3):2 = 5

now we need to find LL' using phytagoras

(LL')² = LN² - (NL')²

LL'² = (√89)² - (13-5)²

LL'² = 89 - 64

LL'² = 25

LL' = 5

since KL' = LL' the triangle of KLL' is isosceles right angle triangle.

so m<LKN = m<LKL' = 45°