We are given the following information:

1. $m\angle ABC$ is 1 degree less than three times $m\angle ABD$.
2. $\angle DBC = 47^\circ$.
3. $m\angle ABC = m\angle ABD + m\angle DBC$, as $\angle ABC$ is the sum of $\angle ABD$ and $\angle DBC$.

Step-by-step solution:

Let:

• $m\angle ABD = x$
• $m\angle ABC = 3x - 1$ (since it's 1 degree less than three times $m\angle ABD$).

We know that: $m\angle ABC = m\angle ABD + m\angle DBC$ Substituting the known values: $3x - 1 = x + 47$

Solving the equation:

1. Simplify the equation: $3x - 1 = x + 47$
2. Subtract $x$ from both sides: $2x - 1 = 47$
3. Add 1 to both sides: $2x = 48$
4. Divide both sides by 2: $x = 24$

Now, calculate the angles:

• $m\angle ABD = x = 24^\circ$
• $m\angle ABC = 3x - 1 = 3(24) - 1 = 72 - 1 = 71^\circ$

Thus:

• $m\angle ABD = 24^\circ$
• $m\angle ABC = 71^\circ$
• $m\angle DBC = 47^\circ$ (given).

Final answer:

• $m\angle ABD = 24^\circ$
• $m\angle ABC = 71^\circ$
• $m\angle DBC = 47^\circ$

Would you like further details or explanations?

Here are some related questions:

1. How do you solve for the unknown angle if multiple angles sum to a known total?
2. What are common strategies for solving equations with angle relationships?
3. How can supplementary and complementary angles be used in problems like this?
4. How can you identify patterns in angle problems involving transversals or parallel lines?
5. What is the importance of defining variables in multi-step angle problems?

Tip: When working with geometric figures, always look for relationships between angles, such as supplementary or complementary pairs, to simplify your calculations.