Question

Compute the value of x in the following figure:

Answer 1

In the given problem, we need to find the value of x

 In the given ΔABC, ∠ACD = 112° and ∠BAE = 120°

Now, BCD is a straight line. So, using the property, “the angles forming a linear pair are supplementary”, we get,

∠ABC + ∠ACD = 180°

      ∠ABC + 112 =  180°

                 ∠ACB = 180° - 112°

                 ∠ACB = 68°

Similarly, EAC is a straight line. So, we get,

∠BAE + ∠BAC = 180°

     120° + ∠BAC = 180°

               ∠BAC = 180° - 120°

               ∠BAC = 60°

Further, using the angle sum property of a triangle,

In ΔABC

∠ACB + ∠BAC + ∠ABC = 180°

             68° + 60° + ∠ABC = 180°

                   128° + ∠ABC = 180° -128°

                              ∠ABC = 52°

Therefore, x = 52°