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Question

I construct quadrilateral with 3 sides and 2 included angles being 75 and 105 respectively and no sides are equal. What is the type of quadrilateral I am constructing?


A

Parallelogram

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B

Trapezium

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C

Square

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D

None of these

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Solution

The correct option is B

Trapezium


The given is 3 sides and 2 included angles
The angles are adjacent angles
Also their sum is 75+105=180
Given angles are supplementary.
Then the remaining two angles are also supplementary. [ Sum of all the angles of a quadrilateral is 3600]
Hence, the quadrilateral is a trapezium as in a trapezium adjacent angles are supplementary angles and since its given no sides are equal , it cannot be a parallelogram( opposite sides are equal) and square, rhombus( all sides are equal)


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