if a quadrilateral is a parallelogram, what are the missing measurements if LM is 45, KL is 31, and angle N 119degrees, What is MN, KN, angle K, angle L, and angle M?
Since the quadrilateral is a parallelogram, opposite sides are equal in length and opposite angles are equal in measure. Therefore, we know that LM = KN = 45, and KL = MN = 31.
Since angle N is 119 degrees, angle L (which is opposite angle N) is also 119 degrees. Similarly, since angle K (which is opposite angle M) is the same as angle L, angle K is also 119 degrees.
Now, using the fact that the sum of the interior angles of a quadrilateral is 360 degrees, we can find angle M:
Angle M = 360 - 119 - 119 - 90 (since angle M and angle L are adjacent angles and form a straight line) = 32 degrees.
Therefore, the missing measurements are:
- MN = 31
- KN = 45
- angle K = 119 degrees
- angle L = 119 degrees
- angle M = 32 degrees