Question

In ΔABC, ∠B = ∠C and ray AX bisects the exterior angle ∠DAC. If ∠DAX = 70°, then ∠ACB =

Options

• 35°

• 90°

• 70°

• 55°

Answer 1

In the given ΔABC, ∠B = ∠C  . D is the ray extended from point A. AX bisects∠DAC and ∠DAX = 70°

Here, we need to find ∠ACB

As ray AX bisects ∠DAC

∠CAX = ∠DAX = 70°

Thus,

∠DAC = ∠DAX + ∠XAC

 = 70° + 70°

= 140°

Now, according to the property, “exterior angle of a triangle is equal to the sum of two opposite interior angles”, we get,

∠DAC = ∠B + ∠C

    140° = 2∠C

   `∠C  =  (140°)/2`

            = 70°

Thus, ∠ACB = 70°