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The interior angles of a quadrilateral (polygon with 4 sides and angles) sum to 360 degrees. We can find this in a couple of ways. First, noting the general formula for an n-gon:
S = (n - 2)(180)
where S is the sum of the interior angles in degrees and n is the number of sides of the n-gon. We find S = (4 - 2)(180) = 360 degrees.
Second, the exterior angles must average 360/n degrees. In this case, 360/4 = 90 degrees. Interior angles are supplementary to exterior angles, so the average interior angle must equal 90 degrees. Finally, 4 interior angles with an average of 90 degrees means a sum of 360 degrees.
Finally, consider some quadrilaterals (e.g. squares, rectangles, parallelograms, etc.). They each contain 360 degrees (e.g. four 90 degree angles).
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What is the sum of all interior angles in a quadrilateral?
i think 360
How many interior angles in a quadrilateral?
There are 4 interior angles in a quadrilateral
Why can't a quadrilateral have no more than three obtuse angles?
The sum of all the interior angles of a quadrilateral is 360 degrees. If it had more than three obtuse angles, then it would have all four angles greater than 90 degrees so that their sum would be greater than 360 degrees.
How can you prove that the sum of the four interior angles in all quadrilaterals equal 360 degrees?
If you accept that the sum of the angles in a triangle is 180 degrees, then picture this. A quadrilateral shape is two triangles. If you draw a line between one pair of opposite corners in quadrilateral shape, you have two triangles that share a common side. The sum of the angles in the quadrilateral must equal the sum of the angles in the two triangles. 2 x 180 = 360
Can you draw a quadrilateral that has three right angles?
The sum of the interior angles of a quadrilateral is 360 degrees. If three of the angles are right angles, that is, of 90 degrees each, the the fourth must be 90 degrees. So you can have a quadrilateral with three right angles but its fourth angle will also be a right angle. So exactly 3 right angles is not possible.
