Question

find the value of x ​

Answer 1

Answer:

The answer will be 30°.

Step-by-step explanation:

We have given;

                    ∠FAE = 75°;

                    ∠ACD = 105°;

Now we are asked for x or ∠ABC;

Now,       ∠FAE = ∠BAC;     (Vertically Opposite Angle)

Hence,   ∠BAC = 75;                                            (i)

Now, angle ACD and angle ACB will form linear pair;

Hence,        ∠ACB + ∠ACD = 180;

                   ∠ACB + 105 = 180;

                   ∠ACB = 180 - 105;

                              = 75;                                        (ii)

Now, we know the angle sum property of a triangle;

that states ;               Sum of all angle = 180;

Hence, in the given triangle,

                              ∠ACB + ∠ABC +  ∠BAC = 180;

   From equation (i) and (ii);

                             ⇒ 75 + x +  75 = 180;

                             ⇒ 150 + x = 180;

                             ⇒ x = 180 - 150;

                             ⇒ x = 30;

Hence, the required angle will be 30.

That's all.