In each of the figures given below, ABCD is a rhombus. Find the value of x and y in each case.
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Class 8
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>>Understanding Quadrilaterals
>>Some Special Parallelograms
>>In the following figures, ABCD is a rhom
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In the following figures, ABCD is a rhombus. Find the values of x and y
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Correct option is A)
In rhombus, Let the line AC and BD intersect at a point called O.
The angle made by this two line at the Center is 90 degree. ( Property of Rhombus)
∠AOB=∠AOD=∠COD=∠COB=90
∠CBD=∠BDA=y ( Alternate Angles)
∠DCA=∠CAB=x ( Alternate Angles)
∴∠DAO=62−x
In triangle AOD,
∠DAO+∠AOD+∠ODA=180
62 - x + 90 + y = 180
y - x = 180 - 90 - 62
y - x = 28
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