# Can a trapezoid have four obtuse angles?explain?

No it can’t. Any quadrilateral, regular or irregular, has a sum of its interior angle measures equal to 360°. An obtuse angle is between 90° and 180°, both exclusive, so if you have four obtuse angles of…say, 90.1°, you have 4(90.1) = 360.4°. You wouldn’t have a polygon in this case because the interior angle sum has been exceeded.

The sum of the four angles in a quadrilateral = what?
How big is an obtuse angle?

Suppose a, b, c, and d are obtuse angles in a trapezoid
Then a > 90, b > 90, c > 90, and d > 90
a + b + c + d > 360
But a + b + c + d = 360, sum of angles of a quadrilateral
Hence a, b, c, and d cannot be obtuse

No. A trapezoid is a quadrilateral which means in part that all four angles must add up to 360 degrees. An obtuse angle is one between 90 an 180 degrees. Thus fours angles greater than 90 degrees means a total greater than 360 degrees which means it is not a quadrilateral and thus not a trapezoid.

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A trapezoid is a type of quadrilateral (a four-sided polygon).