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Question

ABCD is a rhombus, ADC=53. Diagonals AC and BD intersect at O. Find DAO. [3 MARKS]

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Solution

Concept: 1 Mark
Application: 2 Marks

In a rhombus, diagonals bisect the interior angles.

ADO=12(ADC)
ADO=12×53 [Substitute]
ADO=26.5

AOD=90 [Diagonals intersect at right angles]

In AOD,
AOD+ADO+DAO=180 [Angle sum property]
90+26.5+DAO=180
DAO=1809026.5=63.5

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