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

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

Answers (1)

best_answer

Answer: False

Solution.

Acute angle is an angle less than 90^{\circ}
Let all angles of a quadrilateral be acute angles. Now, the smallest acute angle will be equal to 89^{\circ}
Hence sum of all angles = 89^{\circ} + 89^{\circ} + 89^{\circ} + 89^{\circ} = 356^{\circ}
So we can conclude that, if all the angles are less than 90o then the sum of all the angles will be less 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 acute angles.
Hence given statement is False. 

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infoexpert26

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