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avatar+362 

JKL​M  is a parallelogram.

 

What is the measure of ∠KLJ?

 

AngelRay  Nov 4, 2017

Best Answer 

 #1
avatar+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
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4+0 Answers

 #1
avatar+443 
+1
Best Answer

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
avatar+443 
0

(☞ ͡ ͡° ͜ ʖ ͡ ͡°)☞ What do you think of that?

helperid1839321  Nov 4, 2017
 #3
avatar+362 
0

I have to add to get the answer?

AngelRay  Nov 4, 2017
 #4
avatar+1375 
+2

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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