Quadrilaterals and Polygons: Sum of Angles A quadrilateral is a polygon with four sides and four angles. The sum of the angles in a quadrilateral is 360 deg...
Quadrilaterals and Polygons: Sum of Angles
A quadrilateral is a polygon with four sides and four angles. The sum of the angles in a quadrilateral is 360 degrees. This means that the total angle measure of a quadrilateral is equal to 360 degrees.
Examples:
A square has four equal angles, each measuring 90 degrees.
A rectangle has four right angles, each measuring 90 degrees.
A rhombus has four angles that measure 100 degrees each.
Proof:
The sum of the angles in a quadrilateral can be proven using various methods, such as the angle sum theorem. This theorem states that the sum of the angles in a polygon with n sides is equal to 360 degrees.
Applications:
The sum of angles is used in various mathematical and real-world applications, such as:
Calculating the area of a quadrilateral.
Determining the perimeter of a quadrilateral.
Proving geometric theorems.
Additional Notes:
A polygon with n sides is considered a convex polygon if all of its angles are less than 180 degrees.
A polygon with n sides is considered a concave polygon if some of its angles are greater than 180 degrees.
A quadrilateral is a special case of a polygon with four sides and four angles