Question

prove that sum of three angles of triangle is 180°​

Answer 1

Answer:

here

Step-by-step explanation:

Let the triangle be ABC ,

AB + BC + CD = 180

3 = 180

180/3 = x

60 = x

Answer 2

Answer:

Step-by-step explanation:

To prove sum of 3 angles of a triangle is 180°

Proof:

consider a triangle PQR  with angles ∠1,∠2 and ∠3

=> we have to prove that, ∠1 + ∠2 + ∠3 = 180°​

Now draw a line XY such that it is parallel to base ,QR of the triangle and has P as a point in it.   (see attachment)

we have ∠4 and ∠5 formed on the either sides of P with the XY line.

If taken the line PQ as the transversal for the parallel line XY and QR,

then, we have, ∠2 = ∠4   ( as Alternate angles are equal )  --- (1)

similarly,

If taken the line PR as the transversal for the parallel line XY and QR,

then, we have, ∠3 = ∠5   ( as Alternate angles are equal )  --- (2)

We know, ∠4 ,  ∠1 and ∠5 are linear pairs, as they formed on XY

=> ∠4+∠1+∠5 = 180°​   ( sum of linear pair of angles is 180°​ )

by (1) and (2),

=> ∠2+∠1+∠3 = 180°

ie., ∠1+∠2+∠3 = 180°

from the above statement, we can conclude that the sum of angles in a trangle is 180°

Hence proved.