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Upper primary school mathematics question UPQ77

In the figure below, PQTU is a square, TUV is an equilateral triangle and RSTV is a rhombus. Find(a) ∠QRS

(b) ∠PVQ

*Solution:*

TUV is an equilateral triangle,

∠ VTU = ∠ TUV = ∠ UTV = 60^{0}

QTU is right angle,

∠ VTQ = 90^{0} – 60^{0} = 30^{0}

TV = TQ, TVQ form isosceles triangle

∠ QVT = ∠ VQT = (180^{0} – 30^{0}) ÷ 2

∠ QVT = 75^{0}

RSTV is a rhombus,

∠ QRS = 180^{0} – 75^{0} = 105^{0}

Similarly,

∠ PVU = ∠ QVT = 75^{0}

∠ PVQ = 360^{0} – 60^{0} – 75^{0} – 75^{0 }= 150^{0}