Given: KLMN is a parallelogram m∠K : m∠KLM=1:3 LF ⊥ KN , LD ⊥ NM Find: m∠FLD

In a parallelogram, opposite angles are equal and since it is a quadrilateral, the angles add up to 360°

<NKL = <LMN =  X
<KLM = <KNM = 3X
So, 2(x+3x) = 360°
      80x = 360°
       x = 45°
The figure LFND is another quadrilateral where: 
<LFN = <NDL =90°
<FND = 3x

So, (90×2)+3x+ (angle FLD) = 360°
      Angle FLD = 360° - 180° - (3×45)°
                        = 360° - 315°
                        = 45°