the angles of a quadrlateral 180°
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We have seen in the Triangle Sum Conjecture that the sum of the angles in any triangle is 180 degrees. The Quadrilateral Sum Conjecture tells us the sum of the angles in any convex quadrilateral is 360 degrees. Remember that a polygon is convex if each of its interior angles is less that 180 degree.
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The sum of the measures of the interior angles of any quadrilateral can be found by breaking the quadrilateral into two triangles. Since the measure of the interior angles of any triangle equals 180 degrees, each of the two triangles will contribute 180 degrees to the total for the quadrilateral.
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