Since the quadrilaterals are similar, it is found that the measure of angle D is of 92º.
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- If two polygons are similar, their equivalent angles have the same measures.
- Quadrilaterals DEFG and KLMN are similar.
- The angle equivalent to angle D is angle K, thus they are equal.
- The measure of angle D is: (20x + 12)º.
- The measure of angle K is: (25x - 8)º.
Since they are equal:
[tex]25x - 8 = 20x + 12[/tex]
[tex]5x = 20[/tex]
[tex]x = \frac{20}{5}[/tex]
[tex]x = 4[/tex]
Then:
[tex]20x + 12 = 20(4) + 12 = 80 + 12 = 92[/tex]
The measure of angle D is of 92º.
A similar problem is given at https://brainly.com/question/11334173
