Two tangents TP and TQ are drawn from a point T to a circle with centre O…

Step 1. The angle at the centre. $\angle POQ + \angle PTQ = 180^\circ$, so $\angle POQ = 180^\circ - 70^\circ = 110^\circ$.

Step 2. OT bisects the angle at T. $\angle PTO = 70^\circ \div 2 = 35^\circ$.

Step 3. Check. $\angle POT = 110^\circ \div 2 = 55^\circ$, and $35^\circ + 55^\circ + 90^\circ = 180^\circ$.