if angle ABC is one degree less than three times angle ABD and angle DBC = 47 degrees, find each measure.

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.

Explore how to solve angle relationships in triangle ABC with step-by-step solutions. This problem involves understanding angle properties and relationships, suitable for Grades 7-9 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation