Answer:
x = 8
Explanation:
We have the information that lines PQ and ST are parallel
==> m∠RPQ = m∠RTS
since they are alternate interior angles
Also because the two lines are parallel, m∠RST = m∠RPQ
Since angles ∠PRQ and ∠SRT are vertical opposite angles, they are also equal
So triangles PQR and RTS are similar triangles
Similar triangles may have different side lengths but the ratios of their side lengths are the same
In the two triangles we see that RQ = 3cm and RS= 6cm
So the ratio of each side of triangle PQR to the corresponding side is 6/3 = 2
Since side ST corresponds to side PQ, ratio of length of side ST to side PQ is also 2
This means x/4 = 2 or x = 8