Answer:
MK= 12.5
AngleJNK=117°
AngleJNM=63°
Explanation:
Part A:
MN = 3x + 1
JL = 2x + 9
JL and MK are the diagonals
MN = 1/2 of MK
MK =2(3x +1)
MK = 6x + 2
Therefore, JL = MK
2x + 9 = 6x +2
Collect like terms
2x-6x = 2 - 9
-4x = - 7
x = 1.75
Substituting the value of x,
MK = 6(1.75) + 2
MK = 10.5 + 2
MK = 12.5
Part B
AngleJNK = (5x +2)°
AngleJNM = (3x-6)°
Sum of interior angles of a quadrilateral = 360
Therefore, 2(5x +2)° + 2(3x-6)° = 360
(10x + 4) + (6x - 12) = 360
Collect like terms
10x + 6x - 12 + 4=360
16x = 360 + 8
16x = 368
x = 368/16
x = 23
Substituting the value of x
For angleJNK = 5(23) +2 = 115+2 = 117°
For angleJNM = 3(23) - 6 = 69 - 6 = 63°