+633 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.
+633 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.
+2440 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.
