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  • Can all the four angles of a quadrilateral be obtuse angles?  Give reason for your answer.

Can all the four angles of a quadrilateral be obtuse angles?  Give reason for your answer.

Answers (1)

best_answer

Answer: False

Solution.

An obtuse angle is an angle greater than 90^{\circ}
Let all angles of a quadrilateral be obtuse angles. Now, the smallest obtuse angle will be equal to 91^{\circ}
Hence the sum of all angles = 91^{\circ} + 91^{\circ} + 91^{\circ} + 91^{\circ}= 364^{\circ}
So we can conclude that, if all the angles are greater than 90o the sum of all the angles will be greater than 360^{\circ}
But we know that sum of all the angles in a quadrilateral is 360^{\circ}.
Therefore, a quadrilateral can have a maximum of three obtuse angles.
Hence given statement is False.

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