Question

Can all the four obtuse angles form the quadrilateral :
(A) Yes
(B) No
(C) May be
(D) Cannot be determined

Answer 1

Hint: After looking question, to know the condition of obtuse angle is that it should be greater than ${90^0}$ and less than ${180^0}$ i.e. it can be represented as $\angle A\,\, > \,{90^{^0}}\,\,$ and $\angle A\, < {180^0}$. And the sum of angles of any quadrilateral is ${360^0}$ .

Complete step-by-step answer:
As per the given question, there should be known the condition of obtuse angle that is as below :
An angle is to be said as obtuse angle which has angle is greater than ${90^0}$ and less than ${180^0}$ ($\angle A\,\, > \,{90^{^0}}\,\,$and $\angle A\, < {180^0}$ ) known as obtuse angle.
Now let assume four angles as $\angle A\,,\,\angle B\,,\,\,\angle C\,,\,\,\angle D\,\,$. These all are obtuse so it can be represented as an mathematical form as below :
$\angle A\,\, > \,{90^0}$ -------------(1)
$\angle B\,\, > \,{90^0}$ -------------(2)
$\angle C\,\, > \,{90^0}$ -------------(3)
\[\angle D\,\, > \,{90^0}\] -------------(4)
Now we would sum of all equations (1), (2), (3) And (4) and we get result as below :
$ \Rightarrow $ \[\angle A\, + \,\angle B + \angle C + \angle D\,\, > \,{360^0}\] -----------(5)
But we have to check that is that possible with four obtuse angle to draw a quadrilateral, So for it to be any figure as in form of quadrilateral for it condition as given below :
          For any figure is called to be quadrilateral that has sum of four angles should be equal to ${360^0}$. i.e. it can be represented as mathematical format is :
${360^0}$\[\angle A\, + \,\angle B + \angle C + \angle D\,\, = \,\,{360^0}\] ------------(6)
From equation number (5th ) and (6th ) shows that it is not equal. Because the sum of four obtuse angles would be greater than \[{360^0}\] while the sum of four angles in quadrilateral is equal to \[{360^0}\]. So we can say that equation number (5th ) and (6th ) both are contradictory to each other. So we can say that it can not be possible to form a quadrilateral with four angles.

Answer would be option (b).

Note:
In conclusion, for any figure to be quadrilateral, the sum of four angles should be \[{360^0}\]. If there would be three angles obtuse and one angle is acute then it could be possible.