prove that sum of the exterior angles of any quadrilateral is 360 - Maths - Quadrilaterals

Question

prove that sum of the exterior angles of any quadrilateral is 360

Anuradha Sharma · Accepted Answer

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We know that sum of all the angles of a Quadrilateral is 360 degree
So ∠A+∠B+∠C+∠D= 360 degreeNow ∠1= 180-∠A  linear pair  
1∠2= 180-∠B   linear pair    
2∠3= 180-∠C   linear pair    
3∠4= 180-∠D   linear pair    
4Adding, 1, 2, 3, 4, we get ∠1+∠2+∠3+∠4= 180×4- ∠A+∠B+∠C+∠D= 720- 360 = 360 Hence proved