Question

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

• A. Parallelogram
• B. Trapezium
• C. Square
• D. None of these

Answer 1

The correct option is B

Trapezium

The given is 3 sides and 2 included angles
$⟹$ The angles are adjacent angles
Also their sum is ${75}^{\circ }+{105}^{\circ }={180}^{\circ }$
$⟹$ Given angles are supplementary.
Then the remaining two angles are also supplementary. [$\because$ Sum of all the angles of a quadrilateral is ${360}^0$]
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)