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In the diagram, |SP| = |SR| and < PRS = 50o. Calculate < PQR



Dicussion (1)

  • < PRS = RPS = 50\(^{\circ}\) (base of isosceles)
    RPS = 50\(^{\circ}\); < RSP + < PRS + < RPS = 180(sum of < s in a triangle)
    < RPS + 50 + 50 = 180
    < RSP = 180 - 100 = 80
    then < PQR + < RSP = 180 (opp. < S of cyclic quad.)
    < PQR + 80 = 180\(^{\circ}\)
    < PQR = 180 - 80
    = 100

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