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What is the value of x, given that PQ is parallel to BC?

Mathematics
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@Emily778 do you know what is Thales Theorem???

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Other answers:

NO
thales theorem states that \[\huge \frac{AP}{PB}=\frac{AQ}{QC}\]
where AP=8,PB=32,AQ=x and QC=36.
the two triangles are similar, so you can say 8/(32+8) = x/(36+x) solve for x
can you solve it @Emily778
8 x 32?
\[\huge \frac{8}{32}=\frac{x}{36}\] Can you solve for x???
.25
or..Do I cross multiply?
yeah!!
8/(32+8) = x/(36+x) 8/40 = x/(36+x) 8(36+x) = 40x ... ... ... x = ??
288
what x=288????
x=18?
no, wrong
9?
correct
left side you see, 8 is 4 times lees than 32 so right side, 9 has to 4 times less than 36. 9 works.

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