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.
  
• Relationship between Interior and Exterior Angles: At each vertex: Interior Angle + Exterior Angle = 180°

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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