Question

In the following figure, side BC is produced to 'D' and CE llel BA, then show that 1) angleACD =ANGLE'A + ANGLE'B 2) ANGLE1+ANGLE2+ANGLE3=180°

Answer 1

hi friend,
In the Given figure
To prove:-1.∠ACD=∠A+∠B
                2.∠1+∠2+∠3=180°
Proof:∠ACD=∠4+∠5_____________(1)
               ∠4=∠A or ∠1(AIA's)___________(2)
               ∠5=∠B or ∠2(Corresponding angles)___________________(3)
By (1),(2)and (3) we get,
∠ACD=∠A+∠B
________________________________Hence proved__________________
∠3+∠4+∠5=180°(LPA's)
But By (2) and (3) we get,
∠1+∠2+∠3=180°
________________________________Hence Proved__________________
________________________________Thanks :) ______________________