MATH SOLVE

4 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°

<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°