Question

I construct a quadrilateral with 3 sides and 2 included angles which are also adjacent angles and their measures are ${75}^{\circ }$ and ${105}^{\circ }$ 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
• B. Square
• C. Trapezium
• D. Parallelogram

Answer 1

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: ${75}^{\circ }and{105}^{\circ }$.
Their sum is ${75}^{\circ }+{105}^{\circ }={180}^{\circ }$.
Thus, the given angles are supplementary.
Then the remaining two angles are also supplementary. [$\because$ Sum of all the angles of a quadrilateral is ${360}^0$]
So, the quadrilateral can be trapezium or parallelogram.
Parallelogram has been already eliminated.

Hence, the constructed quadrilateral is a trapezium.