Final answer:
By using the principle that the sum of the angles in a triangle is equal to 180 degrees, we set up an equation to solve for x. The value of x was found to be 42.75. Substituting x into the given equation, we found that the value of angle ACB is approximately 55.75 degrees.
Step-by-step explanation:
In this problem, we are given two angles from a triangle: ABC and ACB. Since we know the sum of the angles in a triangle equals to 180 degrees, we can set up the equation (3x - 4) + (x + 13) = 180 to solve for x.
To do this, we combine like terms to get 4x + 9 = 180. Subtracting 9 from both sides, we get 4x = 171. We then divide each side by 4 to solve for x which is approximately 42.75.
Now that we have the value of x, we can find the value of angle ACB. Plugging the value of x into the equation for angle ACB (x + 13), we get 42.75 + 13, which equals to approximately 55.75 degrees. So the angles ABC and ACB are 126.25 and 55.75 degrees, respectively.
Learn more about Angles in a Triangle