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