Interior and Exterior Angles of Quadrilaterals

A quadrilateral is a four-sided polygon. In a quadrilateral, we have both interior and exterior angles, which are related to each other.

The following diagrams show that the sum of interior angles of a quadrilateral is 360° and the sum of exterior angles of a quadrilateral is 360°. Scroll down the page for more examples and solutions on how to find interior and exterior angles of quadrilaterals.

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1. Interior Angles
   

• Definition: The interior angles of a quadrilateral are the angles formed inside the quadrilateral at each of its vertices. A quadrilateral has four interior angles.
  
• Sum of Interior Angles: The sum of the interior angles of any quadrilateral is always 360 degrees.
  This can be proven by dividing the quadrilateral into two triangles by drawing a diagonal. Since the sum of the angles in each triangle is 180 degrees, the sum of the angles in the quadrilateral is 180° + 180° = 360°.
  Formula: Sum of interior angles = (n - 2) × 180°, where ’n’ is the number of sides. For a quadrilateral, n = 4, so (4 - 2) × 180° = 2 × 180° = 360°.
  

2. Exterior Angles
   

• Definition: An exterior angle of a quadrilateral is formed by extending one side of the quadrilateral and the adjacent side.
  
• Relationship with Interior Angles: An exterior angle and its corresponding interior angle are supplementary, meaning they form a linear pair and their sum is always 180 degrees.
  
• Sum of Exterior Angles: The sum of the exterior angles of any quadrilateral, taken in order (one at each vertex), is always 360 degrees. This is true for all convex polygons, including quadrilaterals.
  

Angles in a Quadrilateral question

• Show Step-by-step Solutions

Angles in a Quadrilateral question

• Show Step-by-step Solutions

Angles in a Quadrilateral question

• Show Step-by-step Solutions

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