Answer:
[tex]x=\frac{27}4=6.75[/tex]
Step-by-step explanation:
The triangles PQR and SQT have corresponding angles congruent. In particular the pair P,S, R,T are congruent since corresponding angles relative to the two parallel lines in the hypotesis, and Q is obviously in common. The two triangles are similar since their angles are congruent. We can then write the follwing proportion.
[tex]\overline{RQ}:\overline {TQ}= \overline{PQ}:\overline{SQ}[/tex] Replacing the values and cross-multiplying we get:
[tex](4x-3+3):3=(40+5):5 \rightarrow 4x:3 = 45:5 \\4x=27 \rightarrow x=\frac{27}4=6.75[/tex]
