Question

Which of the following is a valid quadrilateral?

(a) ▀ABCD ∠A=60,∠B=120,∠C=120,∠D=90

(b) ▀PQRS ∠A=90,∠B=90,∠C=90,∠D=90

(c) ▀LMNO ∠A=90,∠B=150,∠C=90,∠D=60

(d) ▀EFGH ∠A=120,∠B=120,∠C=120,∠D=120

The question was posed to me in my homework.

The origin of the question is Geometry topic in chapter Practical Geometry of Mathematics – Class 8

Answer 1

Right choice is (b) ▀PQRS ∠A=90,∠B=90,∠C=90,∠D=90

For explanation I would say: The basic property of any quadrilateral is that the sum of all the internal angles is 360°. Here except ▀PQRS the sum of all the internal angles of other quadrilaterals is greater than 360°. Hence all the other quadrilateral other then ▀PQRS are incorrect.