The statements that must be true based on the figure given are: a. 8 c. 52 d. KL ≅ ML.
How to find the value of x?
The image (see attachment for missing image) shows two congruent triangles that share a common side, hence, every corresponding parts of the triangles are equal.
Thus, we can find x by creating the following equation:
KN = MN
Plug in the values:
7x - 4 = 5x + 12
Solve for x:
7x - 5x = 4 + 12
2x = 16
x = 16/2
x = 8
MN = 5x = 12 = 5(8) + 12
MN = 52
KN will also be equal to 52.
Sides KL and ML. are also congruent. The correct options would be, A, C, and D.