Answer :

Given: TQR = 40° and SPR = 30°.


QTR = 90° (right angle)


As we know, using theorem (1), in any triangle, sum of the three interior angles is 180 °.


So,


TQR + QTR + TRQ = 180°


40° + 90° + TRQ = 180°


TRQ = 180° - 40° - 90°


TRQ = 50°


TRQ = TRS = 50°


Also,


SPR + PRS + RSP = 180°


SPR + TRS + RSP = 180°


30° + 50° + RSP = 180°


RSP = 180° - 30° - 50°


RSP = 100°


As R, S and Q lie on the same line.


So,


RSP + PSQ = 180°


PSQ + 100° = 180°


PSQ = 80°


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