Question

plzz .................... urgent .....​

Answer 1

Answer:

13.

Given :

A triangle ABC.

To prove :

∠A+∠B+∠C=180°

⟹∠1+∠2+∠3=180°

Construction :

Through A, draw a line l parallel to BC.

Proof :

Since l∥BC. Therefore,

∠2=∠4 .......eq(i)

And, ∠3=∠5......eq(ii)

adding eq(i)and(ii)

Therefore, ∠2+∠3=∠4+∠5

∠1+∠2+∠3=∠1+∠4+∠5 [adding∠1bothSide]

∠1+∠2+∠3=180°

Thus, the sum of three angles of a triangle is 180°

12.

Answer

If two lines i.e. AB & CD intersect each other. They have two pair of opp. angles.

i.e.

∠AOC,∠DOB,∠AOB,∠COB.

To prove :- ∠AOC=∠DOB & ∠AOD=∠COB

Proof :-

∠AOC+∠AOD=180

∘

[linear pair] ___(1)

∠AOD+∠BOD=180

∘

[linear pair] ___(2)

from eq. (1) & (2)

∠AOC+∠AOD=∠AOD+∠BOD

i.e. [∠AOC=∠BOD]

Similarly [∠AOD=∠COB] Hence proved.