Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
(N/A) No,all four angles of a quadrilateral cannot be obtuse angles.
An obtuse angle is an angle greater than $90^{\circ}$.
If all four angles were obtuse,each angle would be $> 90^{\circ}$.
Therefore,the sum of the four angles would be $> 90^{\circ} + 90^{\circ} + 90^{\circ} + 90^{\circ} = 360^{\circ}$.
However,the sum of the interior angles of a quadrilateral is always exactly $360^{\circ}$.
Since the sum cannot exceed $360^{\circ}$,it is impossible for all four angles to be obtuse.
An obtuse angle is an angle greater than $90^{\circ}$.
If all four angles were obtuse,each angle would be $> 90^{\circ}$.
Therefore,the sum of the four angles would be $> 90^{\circ} + 90^{\circ} + 90^{\circ} + 90^{\circ} = 360^{\circ}$.
However,the sum of the interior angles of a quadrilateral is always exactly $360^{\circ}$.
Since the sum cannot exceed $360^{\circ}$,it is impossible for all four angles to be obtuse.
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