Question

proof that the sum of the angles of triangle is 180°​

Answer 1

Given: A triangle ABC having angles.. $\angle2$, $\angle4$ and $\angle5$

Construction: Draw a line parallel to BC which passes from A to BC.

Such that BC || MN.

$\bold{To\:Prove:}$ $\angle2$ + $\angle4$ + $\angle8$ = 180°

Solution:

By construction MN is a line parallel to BC.

So..

=> $\angle1$ + $\angle2$ + $\angle3$ = 180° _____ (eq 1)

Now..

MN || BC with transverse AB.

=> $\angle4$ = $\angle1$ (Alternative interior angles) _____ (eq 2)

Also; MN || BC with transverse AC.

=> $\angle3$ = $\angle5$ (Alternative interior angles) _____ (eq 3)

______________________________

• We have (eq 1) i.e.

=> $\angle1$ + $\angle2$ + $\angle3$ = 180°

» Put values of (eq 2) and (eq 3) in (eq 1)

=> $\angle2$ + $\angle4$ + $\angle8$ = 180°

__________ [HENCE PROVED]

Answer 2

Answer:

hope.it will.help your