Given the problem, let's define the angles as follows:

• Let the measure of angle $\text{ABD}$ be $x$.
• Therefore, the measure of angle $\text{ABC}$ is $3x - 1$ (since it's one degree less than three times angle $\text{ABD}$).
• Angle $\text{DBC}$ is given as $47^\circ$.

Since $\text{ABC}$ is the sum of angles $\text{ABD}$ and $\text{DBC}$, we can write:

$\text{ABC} = \text{ABD} + \text{DBC}$

Substituting the values we have:

$3x - 1 = x + 47$

Now, solve for $x$:

$3x - x = 47 + 1$ $2x = 48$ $x = 24^\circ$

Now that we have $x$, which is the measure of angle $\text{ABD}$, we can find the measure of angle $\text{ABC}$:

$\text{ABC} = 3x - 1 = 3(24) - 1 = 72 - 1 = 71^\circ$

Thus, the measures of the angles are:

• $\text{ABD} = 24^\circ$
• $\text{ABC} = 71^\circ$
• $\text{DBC} = 47^\circ$ (already given)

Would you like further details on this solution, or do you have any questions?

Here are 5 related questions:

1. What would happen if $\text{DBC}$ were a different angle?
2. How would the solution change if angle $\text{ABC}$ were four times angle $\text{ABD}$ instead of three times?
3. Can you determine the type of triangle $\text{ABC}$ forms if all angles are known?
4. How does this problem relate to the exterior angle theorem?
5. What if angle $\text{ABC}$ was expressed as a sum of $\text{ABD}$ and twice $\text{DBC}$?

Tip: When dealing with angle problems, always write down what each variable represents and relate all given angles to find the unknowns step by step.