Question

Is it possible to construct a quadrilateral ROAM in which RO = 4 cm, OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°? If not, why?

Answer 1

Given measures are OA = 5 cm, ∠O = 120°, ∠R = 105° and ∠A = 135°

Here, we see that, ∠O + ∠R + ∠A = 120° + 105° + 135° = 360°

i.e. the sum of three angles of a quadrilateral is 360°.

This is impossible, as the total sum of angles is 360° in a quadrilateral.

Hence, this quadrilateral cannot be constructed.