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Given: KLMN is a parallelogram m∠K : m∠KLM=1:3 LF ⊥ KN , LD ⊥ NM...
5 months ago
Q:
Given: KLMN is a parallelogram m∠K : m∠KLM=1:3 LF ⊥ KN , LD ⊥ NM Find: m∠FLD
Accepted Solution
A:
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°