If the side BC of Δ ABC is produced on both sides, then write the difference between the sum of the exterior angles so formed and ∠A.

Given that,

BC produced on both sides

We know that,

A + ABC + ACB = 180o (i)

ABD = A + ACB (Exterior angle theorem) (ii)

ACE = A + ABC (Exterior angle theorem) (iii)

Adding (ii) and (iii), we get

ABD + ACE = A + (A + ACB + ACB)

ABD + ACE = A + 180o

(ABD + ACE) - A = 180o

Thus, between the sum of the exterior angles so formed and A is 180o.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Lines and Angles43 mins
Quiz | Lines and Angles40 mins
Quiz | Angle Sum Property of Triangle40 mins
NCERT | Angle Sum Property44 mins
Lines and Angles45 mins
Matter and Its Classification34 mins
NCERT | Intersecting and Non Intersecting lines)41 mins
NCERT | Discussion on Lines And Angles45 mins
Know About Transversal and Parallel lines42 mins
Champ Quiz | Triangle Inequality27 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses