Question

prove that all angles of triangle is 180°​

Answer 1

A triangle's angles add up to 180 degrees because one exterior angle is equal to the sum of the other two angles in the triangle. In other words, the other two angles in the triangle (the ones that add up to form the exterior angle) must combine with the third angle to make a 180 angle.

Answer 2

Answer:

QUESTION : prove that all angles of triangle is 180°.

Given : ∆PQR with angles , angle 1, angle 2 and angle 3.

Prove : angle 1+ angle 2+ angle 3 = 180°

Construction : draw a line XY passing through P parallel to QR .

Proof : For lines XY and QR

with transversal PQ

angle 2 = angle 4 --------------(alternate angle)............ equation no 1.

For lines XY and QR

and QR with transversal PR.

angle 3 = angle 5---------------(alternate angle)............. equation no 2.

also ,for line XY .

angle 1+angle 4 + angle 5 = 180°............(linear pair)

angle 1 + angle 2 + angle 3 = 180°...........

( from equation 1and 2)

hence, sum of all angles of a triangle are equal.

HENCE PROVED.