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Question

In the diagram, ABCD is a rhombus. AEC and BED are straight lines. Find the value of p+q+r+s+t


A
200
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B
270
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C
360
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D
540
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Solution

The correct option is B 270
In the rhombus ABCD,
A+B+C+D=360 [Angle sum property]

The diagonals of a rhombus bisect the angles at the vertex.
DAC=CAB=12DAB
p=12A
A=2p

Similarly, B=2q, C=2t and D=2s
2p+2q+2t+2s=360
p+q+t+s=180

The diagonals of a rhombus intersect at 90
AEB=r=90

Thus, p+q+r+s+t=180+90
p+q+r+s+t=270

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