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Upper primary school mathematics question UPQ78

ABCD is a parallelogram. ADE is a straight line and DC = DE. Find ∠ x and ∠ y.

*Solution:*

ABCD is a parallelogram,

∠ CDE = ∠ BAD = 78^{0}

DC = DE, CDE form a isosceles triangle,

∠ CED = ∠ ECD = (180^{0} – 78^{0}) ÷ 2 = 51^{0}

ADE is a straight line,

∠ x = 180^{0} – 51^{0} = 129^{0}

ABD is a triangle,

∠ ABD + ∠ ADB = 180^{0} – 78^{0} = 102^{0}

ADE is a straight line,

∠ ADF = 180^{0} – 150^{0} = 30^{0}

BFD is a triangle,

∠ y = 180^{0} – (∠ ABD + ∠ ADB) – ∠ ADF – 36^{0}

= 180^{0} – 102^{0} – 30^{0 }– 36^{0 }= 12^{0}