Question

Can a quadrilateral ABCD be a parallelogram if

i. Angle D + Angle B = 180°​​

Answer 1

Step-by-step explanation:

(i) ∠D+∠B=180

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?

(ii) AB=DC=8 cm, AD=4 cm and BC=4.4 cm?

(iii) ∠A=70

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and ∠C=65

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Answer 2

Yes, in a parallelogram an angle which is acute is always adjacent to an angle which is obtuse(by construction) on both sides.

If we follow this rule and consider Angle D an obtuse of 100° and Angle B an acute angle of 80°

Then It can be equal to 180°.

OR

Let angle B = 80° , D = 100°

Opposite angles in a parallelogram are equal.

angle A = 100 , C = 80°

The sum of all angles is 360° hence the shape is possible.

But if we take angle D = 101°

101+101+80+80 > 360 which is not possible.

Hence a quadrilateral can be parallelogram if angle D+B =180°