Question

Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, $\angle O={120}^{\circ },\angle R={105}^{\circ }$ and $\angle A={135}^{\circ }$? If not, why?

Answer 1

No,
Given measures are
OA = 5 cm, $\angle O={120}^{\circ },\angle R={105}^{\circ }$ and $\angle A={135}^{\circ }$
Here, we see that, $\angle O+\angle R+\angle A={120}^{\circ }+{105}^{\circ }+{135}^{\circ }={360}^{\circ }$
i.e. the sum of three angles of a quadrilateal is ${360}^{\circ }$.
This is impossible, as the total sum of four angles is ${360}^{\circ }$ in a quadrilateral.
Hence, this quadrilateral cannot be constructed.