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# JKL​M is a parallelogram.

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JKL​M  is a parallelogram.

What is the measure of ∠KLJ?

AngelRay  Nov 4, 2017

#1
+443
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Since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.

helperid1839321  Nov 4, 2017
Sort:

#1
+443
+1

Since KLJ is a parallelogram, it can be split into 2 congruent triangles, as seen above. The angles remain the same, so we know angle KJL is also 25 degrees. Using the triangle angle sum theorem (all sides of a triangle add up to 180 degrees), we can determine the missing angle measure is 25 degrees. It would have been nice if the question told us JKLM was also a rhombus.

helperid1839321  Nov 4, 2017
#2
+443
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(☞ ͡ ͡° ͜ ʖ ͡ ͡°)☞ What do you think of that?

helperid1839321  Nov 4, 2017
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+362
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AngelRay  Nov 4, 2017
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+1375
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It does not matter if the parallelogram is a rhombus; it makes no difference.

A property of a parallelogram is that opposite sides are parallel. This means that $$\overline{JK}\parallel\overline{ML}$$. By the alternate interior angles theorem, $$\angle MLJ\cong\angle LJK$$. This indicates that both angles are also of equal measure. Therefore, $$m\angle MLK=m\angle LJK=25^{\circ}$$

By the triangle sum theorem, the sum of all the angles in a triangle is equal to 180 degrees. Using this rule, we can solve for the measure of the remaining angle.

 $$m\angle KLJ+m\angle LJK+m\angle JKL=180$$ Substitute the known values in for the angles. $$m\angle KLJ+25+130=180$$ Now, solve for the only unknown. $$m\angle KLJ+155=180$$ $$m\angle KLJ=25^{\circ}$$

Yes, you have to do basic addition and subtraction to get the answer to this problem. And as helperid1839321 mentioned, because the diagonals of the parallelogram bisect a pair of opposite angles, this figure is a rhombus.

TheXSquaredFactor  Nov 5, 2017

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