Is it possible to construct a quadrilateral ABCD in which AB = 5 cm, BC = 7.5 cm, ∠ A = 80°, ∠ B = 140° and ∠ C = 145°? If not, give reason.

Question

Is it possible to construct a quadrilateral ABCD in which AB = 5 cm, BC = 7.5 cm, &#x2220; A = 80&#x00b0, &#x2220; B = 140&#x00b0 and &#x2220; C = 145&#x00b0? If not, give reason.

Philoid · Accepted Answer

No, it is not possible to construct a quadrilateral ABCD with the given measurements. ∠ A + ∠ B + ∠ C (= 80° + 140° + 145° = 365° ) is greater than 360° .The sum of all the four angles is 360° , quadrilateral cannot be constructed.