Let’s write the value of x in each of the following figure.

The given figure is as shown below:

Given ∠PQT = 55°, ∠RST = 60°

To find the angle, i.e., ∠TRS = x°

Now in the given figure PQ is parallel to TS, so

∠PQT = ∠RTS as they form is alternate interior angles.

So ∠RTS = 55°….(i)

Now consider ΔRTS,

We know in a triangle the sum of all three interior angles is equal to 180°.

So in this case,

∠RTS + ∠TRS + ∠RST = 180°

Substituting the values from given criteria and equation(i), we get

55° + ∠TRS + 60° = 180°

⇒ ∠TRS = 180° - 60° - 55°

⇒ ∠TRS = 65°

So the measurement of unknown angle in the given figure is 65°.