In parallelogram JKLM , diagonals KM and JL meet at point N . The length of KM is equal to 5x+1 units. The length of NM is equal to 2x+9 units. What is the value of x? (1 point) units
Since JKLM is a parallelogram, we know that the opposite sides are congruent.
Therefore, KJ = LM.
Similarly, we know that the opposite sides are parallel, so MK || JL.
Therefore, by the corresponding angles formed by the transversal, we know that ∠KNM = ∠JML.
By the same logic, we know that ∠JNM = ∠MKL.
Since ∠KNM and ∠JNM are corresponding angles, they are congruent.
By the same logic, ∠JML and ∠MKL are congruent.
Therefore, we have two pairs of congruent angles, so triangles KJN and LNM are similar by AA similarity.
By the properties of similar triangles, we know that the corresponding sides are in proportion.
Therefore, KM/NM = KJ/LN.
Plugging in the given values, we have (5x+1)/(2x+9) = KJ/LN.
Cross multiplying, we have KJ(NM) = LN(KM).
Plugging in the given values, we have KJ(2x+9) = LN(5x+1).
Since KJ = LM, we have (2x+9) = (5x+1).
Now we solve this equation for x.
Expanding the equation, we have 2x + 9 = 5x + 1.
Subtracting 2x from both sides, we have 9 = 3x + 1.
Subtracting 1 from both sides, we have 8 = 3x.
Dividing both sides by 3, we have x = 8/3.
Therefore, the value of x is 8/3 units.