The rectangle's length LN is 18, and the angle ∠LKMLN measures 126 degrees, derived from the properties of equal diagonals and angle relationships in the given quadrilateral.
The solution begins by establishing properties of a rectangle, stating that its diagonals are equal and bisect each other. The equation 3x + 12 = 2(276 + 2) is then solved to find x, yielding x = 87. Substituting this value, the length LN of the rectangle is determined as 18.
To show that JN = MN, the equality of angles ∠NTM and ∠LNMS is asserted based on the angles opposite equal sides. The calculation further demonstrates that ∠INIMOLN75 = 27 degrees.
Using the fact that the sum of angles in a quadrilateral is 360 degrees, the solution examines the angles in quadrilateral NAJN, leading to the determination of ∠LJNM as 126 degrees, which is a vertical opposite angle to ∠LKMLN.
In summary, the length LN of the rectangle is found to be 18, and the angle ∠LKMLN is determined as 126 degrees.
The question probable may be:
In the rectangle below, JN=2x+2 , K M=3x+12 , and m∠ NJM=27°. Find LN and m∠ KNL.