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

Rhombus

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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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