We can find this by first doing 180 - 146 = 34° = angle TSQ. We know that triangle TSQ is an isosceles triangle as TS = TQ, which means we can then multiply 34 by 2 to get 68, and subtract it from 180 to get 112° as angle STQ.
Then we can use the rule that angles on a straight line add to 180° and do 180 - 112 = 68° = angle RTS. Now we must see the quadrilateral RTSP, and therefore the rule that all interior angles in a quadrilateral add up to 360° can be applied.
Because PQ = PR, that makes triangle PRQ an isosceles triangle and so angle RPQ would be equal to angle QRP. If we call angle RPQ 'x', we can then write an equation to solve:
146 + 68 + x + x = 360 2x + 214 = 360 - 214 2x = 146 ÷ 2 x = 73
