Yes correct

May I know what is the name of the angle RPSQ

It is called reflex angle PSQ

alternative method (and probably the method they expect since they don't expect P6 to know angle sum of quadrilateral = 360°)

angle SPQ + angle SQP = 180° - 110° = 70°
(angle sum of triangle PSQ)

angle RQP + RPQ

= angle SPQ + angle SQP + angle RPS + angle RQS

= 70° + 10° + 10°
= 90°

Angle PRQ = 180° - 90° (angle sum of triangle PRQ)

= 90°

Another alternative solution :


angle PSQ = 110°

Since sum of angles at a point = 360°,

Then

angle PSQ + reflex angle PSQ = 360°

110° + reflex angle PSQ = 360° ①

But sum of angles in a quadrilateral also= 360° (the one you've used in your working)

So,

angle RPS + angle RQS + angle PRQ + reflex angle PSQ = 360°

Which means that :

10° + 10° + angle PRQ + reflex angle PSQ = 360°

20° + angle PRQ + reflex angle PSQ = 360°②

Notice that both equations ① and ② have reflex angle PSQ in common and that angle sum is equal to 360°

This tells you that :

20° + angle PRQ = 110°

so angle PRQ = 110° - 20° = 90°