Question

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Answer 1

Answer:

75 x 30 then it is the answer

Answer 2

Answer:  x = 45°

In the fig.,

∠BAF = ∠DEF = 75° .........(corresponding angles)

also,  ∠DEF + ∠CEF = 180° ........(linear pair angle are 180°)

      ∴     75°  + ∠CEF = 180°

      ∴     ∠CEF = 105°

now, in Δ CEF ,

                 ∠C + ∠F + ∠CEF = 180° ......(angle sum property of Δ)

                   x + 30° + 105° = 180°

                   x = ∠C = 45°

Step-by-step explanation: (Theorem Proof)

Consider a triangle ABC (See in image attached with answer).

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°

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