The measure of the angle m∠FLD is 45 degrees.
A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. The given figure shows a parallelogram ABCD which as AB parallel to CD and AD parallel to BC.
In a parallelogram, opposite angles are equal and since it is a quadrilateral, the angles add up to 360°.
[tex]\rm \angle NKL = \angle LMN = X\\\\\angle KLM = \angle KNM = 3X\\\\ 2(x+3x) = 360\\\\ 80x = 360\\\\ x=\dfrac{360}{80}\\\\ x = 45[/tex]
The figure LFND is another quadrilateral where:
[tex]\rm \angle LFN = \angle NDL =90\\\\ \angle FND = 3x[/tex]
The measure of the, m∠FLD is;
[tex]\rm (90\times 2)+3x+ (angle\ FLD) = 360\\\\m \angle\ FLD = 360- 180- (3\times 45)\\\\ m \angle\ FLD = 360 - 315\\\\ m \angle\ FLD = 45[/tex]
Hence, the measure of the angle m∠FLD is 45 degrees.
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