passpadi

2002

Mathematics

JAMB

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°

Correct Answer: 24°

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 = 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 = 72/3 x = 24°
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