I see you've uploaded a geometry problem. This seems to be a set of four different triangle-related problems, asking to find the value of $x$ in each case. Let me go over each part one by one.

Problem Breakdown:

a) Triangle $ABC$

• The triangle has a line segment drawn parallel to side $BC$, dividing the triangle into two smaller triangles.
• $M$ and $N$ are points on side $BC$, with given segment lengths.
• The relation between the segments $AM$ and $MN$ suggests that this might be a case of similar triangles or the proportionality theorem.

b) Triangle $KLM$

• The smaller triangle $KLM$ is similar to the larger triangle, with line $ON \parallel LM$ (suggesting the use of the basic proportionality theorem).
• The segments $KN$ and $LM$ are given.

c) Triangle $PQR$

• It seems that there is another triangle where similar triangles or parallel lines might be involved.
• The relation between segments $PQ$, $QR$, and $ST \parallel QR$ will likely help find $x$.

d) Triangle $ABMN$

• This is a right triangle with a perpendicular height and another line intersecting it. The segments are likely proportional.

Would you like me to proceed with solving the problems step by step? Let me know if you need any clarifications or further details.