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

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72${}^{\circ }$, find x

Answer Details

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 = 24${}^{\circ }$