Respuesta :

Answer: 14

Step-by-step explanation:

We know that [tex]\triangle SRV \con \triangle QRV[/tex] by SAS, so this means [tex]QV=SV[/tex] by CPCTC. Hence, [tex]4x-1 \longrightarrow x=4[/tex].

We also know that [tex]\triangle STR \cong \triangle QTR[/tex] by SAS, so this means [tex]TS=TQ[/tex] by CPCTC. Since [tex]TS=3x+2=3(4)+2=14[/tex], TQ=14.

Check the picture below.

we know that SR = RQ, we also know the angles at the point R are four right angles, triangles TRS and TRQ are sharing the same side of TR, that makes those two triangles congruent triangles by right-triangles LL theorem.

Likewise, triangles VRS and VRQ are sharing the side RV and thus those triangles are also congruent triangles by right-triangles  LL theorem.

due to congruent triangles, then TQ = 3x+2 and 4x-1 = 15.

Ver imagen jdoe0001