Question

The sides of a triangle ABC are produced in order to form

the exterior angles 1, 2, 3. Show that ∠1 +∠2 + ∠3 = 360°.​

Answer 1

ABC + ∠CBF = 180° [Linear pair]………..(i) 

∠ACB + ∠ACD = 180° [Linear pair]……(ii) 

∠BAC + ∠BAE = 180° [Linear pair]…….(iii) 

Byadding(i), (ii) and (iii) 

∠ABC + ∠CBF + ∠ACB + ∠ACD+ ∠BAC + ∠BAE = 180 + 180 + 180 

∠ABC + ∠ACB + ∠BAC + ∠CBF + ∠ACD + ∠BAE = 540°  180° + ∠CBF + ∠ACD + ∠BAE = 540° 

[Sum of the angles of a triangle 180°] 

∠CBF + ∠ACD + ∠BAE = 360°Read more on