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Upper primary school mathematics question UPQ58

In the figure below, not drawn to scale, MNOP is a rhombus. Find ∠ *x*.

*Solution:*

A rhombus, MN // PO and MP // NO

∠ PMN + ∠ MNO = 180^{0}

∠ PMN = 180^{0} – 110^{0} = 70^{0}

Line MO bisects ∠ PMN,

∠ OMN = 70^{0} ÷ 2 = 35^{0}

∠ *x* = 180^{0} – 35^{0} – 130^{0} = 15^{0}

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