In the figure above, PQR is a straight line segment, PQ = QT. Triangle PQT is an isosceles triangle, ∠SQR is 75 and ∠QPT is 25

. Calculate the value of ∠RST.

  • A 45°
  • B 55°
  • C 25°
  • D 50°
jamb 2001mathematics

The correct answer is B. 55°

In Δ PQT,

∠PTQ = 25

(base ∠s of isosceles Δ)

In Δ QSR,

∠RQS = ∠QPT + ∠QTP

(Extr = sum of interior opposite ∠s)

∠RQS = 25 + 25

= 50

Also in Δ QSR,

75 + ∠RQS + ∠QSR = 180

(sum of ∠s of Δ)

∴75 + 50 + ∠QSR = 180

125 + ∠QSR = 180

∠QSR = 180 - 125

∠QSR = 55

But ∠QSR and ∠RST are the same

∠RST = 55

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