Given ABC with incenter D, find mACD if mACB = 3x + 54 and m ACD = x + 31.

Given:

In triangle ABC, D is incenter m∠ACB = 3x + 54 and m∠ACD = x + 31.

To find:

m∠ACD.

Solution:

We know that,

Incenter of a triangle is the intersection point of all angle bisectors.

     ...(i)

Now,

      [Using (i)]

Substitute the values, we get

The value of x is 8.

Therefore, the measure of angle ACD is 39 degrees.

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