Can A Trapezoid Have 4 Obtuse Angles? Explain.


5 Answers

Oddman Profile
Oddman answered
A trapezoid is a quadrilateral. The sum of the interior angles of a quadrilateral is 360°. Four angles whose measure is greater than 90° will sum to a number that is greater than 360°. So, no quadrilateral (including a trapezoid) can have four obtuse angles.
Brooke Mundy Profile
Brooke Mundy answered
No that would be impossible.Since it is a quadrilateral, the sum of the angles must equal 360 degrees. To be considered obtuse, an angle must be greater than 90 degrees.
Zhu Yugang Profile
Zhu Yugang answered
No,it can't.It has two sides which is parallel,the sum of the two Angles are 180 degree,so all the Angles are Obtuse Angle is impossible.
Simon Templar Profile
Simon Templar answered
A trapezoid is a quadrilateral with two parallel sides.

Depending upon whether you're dealing with an Euclidean geometry, would dictate whether your scenario were possible.  In flat-surface, or Euclidean geometry, the sum of the four angles in a trapezoid are 360.  In non-flat-surface, or non-Euclidean geometry, you have curved space, upon which interesting angular relationships show up.  And it would have to be in a non-Euclidean situation for there to be more than two obtuse angles in a trapezoid.

You are likely not taking a non-Euclidean geometry class.  So, for you, the answer would be: No.

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