If the sides of a quadrilateral are produced in order, what is the sum...
When the sides of a quadrilateral are extended, each exterior angle is the supplementary angle to its interior angle. The sum of the exterior angles of any convex polygon is always 360° because each exterior angle represents a turn around the shape, and all turns together make one full circle. Hence, the sum of the exterior angles of a quadrilateral is 360°.
If the sides of a quadrilateral are produced in order, what is the sum...
Understanding Exterior Angles of a Quadrilateral
When we talk about a quadrilateral, we refer to a polygon with four sides. When the sides of this quadrilateral are extended, they create exterior angles at each vertex. The question asks for the sum of these exterior angles.
Concept of Exterior Angles
- An exterior angle is formed when a side of a polygon is extended.
- For any polygon, the exterior angle at each vertex is equal to 180° minus the interior angle at that vertex.
Sum of Exterior Angles Formula
- The important property to remember is that the sum of the exterior angles of any polygon, regardless of the number of sides, is always 360°.
- This rule holds true for a quadrilateral, as well as for any other polygon.
Why is the Sum Always 360°?
- As you move around the polygon, each time you make a turn at a vertex (exterior angle), you are effectively turning a total of 360 degrees to return to your starting point.
- Hence, no matter how many sides the polygon has, the total amount of rotation (and therefore the total of the exterior angles) remains constant at 360°.
Conclusion
In conclusion, when the sides of a quadrilateral are produced in order, the sum of the exterior angles formed is always:
- 360°
Thus, the correct answer is option A. This fundamental property is not only crucial for understanding quadrilaterals but also applies to polygons of any shape and size.