Question

8- Prove that the sum of all angles of a triangle is 180​

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

The sum of all angles of triangle is 180°.

Given: PQR with angles ∠1,∠2and∠3

Prove: ∠1+∠2+∠3=180°

Construction: Draw a line XY passing through P parallel to QR

Proof:

For lines XY&QR,                       For lines XY&QR

with transversal PQ                   with transversal PR

∠2=∠4 (Alternate angles)            ∠3=∠5 (Alternate angles)  

Also, for line XY

∠1+∠4+∠5=180°           (Linear pair)

∠1+∠2+∠3=180°           (From (1) and (2)

Hence, sum of all angle of triangles are equal.

Hence proved.