In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72°, find x

  • A 36°
  • B 18°
  • C 72°
  • D 24°
jamb 2002mathematics

The correct answer is D. 24°

In Δ PQS, ∠PSQ = X(base ∠s of isoc Δ PQS)

In Δ QRS, ∠RQS = ∠PSQ + X(Extr ∠ = sum of two intr. opp ∠s)

∴ ∠RQS = X + X= 2X

Also ∠QRS = 2X(base ∠s of isoc Δ QRS in Δ PRS,

72 = ∠RPS + ∠PRS(Extr, ∠ = sum of two intr. opp ∠s)

∴ 72 = x + 2x

72 = 3x

x = 24

Previous question Next question