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Question

I construct a quadrilateral with 3 sides and 2 included angles which are also adjacent angles and their measures are 75 and 105 respectively. No sides are equal and one pair of opposite sides are parallel in this quadrilateral. What is the type of quadrilateral I am constructing?

A
Rhombus
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B
Square
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C
Trapezium
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D
Parallelogram
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Solution

The correct option is C Trapezium
Since, no sides are equal then, the quadrilateral can't be parallelogram, square and rhombus.

Also, we have been given 2 included angles which are adjacent.
Two included angles are: 75and 105.
Their sum is 75+105=180.
Thus, the given angles are supplementary.
Then the remaining two angles are also supplementary. [ Sum of all the angles of a quadrilateral is 3600]
So, the quadrilateral can be trapezium or parallelogram.
Parallelogram has been already eliminated.

Hence, the constructed quadrilateral is a trapezium.

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