Mathematics

In the diagram above, PST is a straight line, PQ = QS = RS. If…

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72o, find x
  • A.
    36o
  • B.
    18o
  • C.
    72o
  • D.
    24o
Correct Answer: Option D
Explanation

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 = 72/3
x = 24o