Q10 of 31 Page 4

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.

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.

More from this chapter

All 31 →
8 Construct a quadrilateral PQRS in which QR = 7.5 cm, RP = PS = 6 cm, RS = 5 cm and QS = 10 cm. 9 Construct a quadrilateral ABCD in which BC = 5.5 cm, CD = 4 cm, ∠ A = 70°, ∠ B = 110° and ∠ D = 85°. 11 Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 3.5 cm, CD = 5 cm, ∠ B = 450 and ∠ C = 150°.  1

The diagonals of a parallelogram are not perpendicular. Is it a rhombus? Why or why not?