Question

What is the length of segment TQ?

Answer 1

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.

Answer 2

Answer: 14

Explanation:

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

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