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In δAbc, ∠B = ∠C and Ray Ax Bisects the Exterior Angle ∠Dac. If ∠Dax = 70°, Then ∠Acb = - Mathematics

MCQ

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

Options

  • 35°

  • 90°

  • 70°

  • 55°

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Solution

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°

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 11 Triangle and its Angles
Q 6 | Page 25
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