Question

prove that if a side of a triangle is produced then the exterior angle so formed is equal to the sum of two interior opposite angles

Answer 1

in a triangle ∆ABC
E is produced on BC
IN ∆ABC
<BAC + <ACB + <CBA = 180
( sum of angle property) (1)
<ACB + <ACE = 180
( LINEAR PAIR ) (2)
eq1 and eq2 is equal to 180
<BAC + <ACB+ <CBA = <ACB + <ACE
<ACB will be cut from both side
<BAC + <CBA = <ACE

hence proved

Answer 2

Given: angle p+q+r=180°

to prove: angle s =p+q

proof: angle r+ angle s=180°(linear pair)---1

angle p+q+r=180°(angle sum property)---2

from 1 and 2

r+s=p+q+r

hence, r=r

s=p+q. proved