https://file.aiquickdraw.com/mathbot/file/1727393534419lb42qz8y.jpg

The diagram shows two angles sharing a vertex \( B \). You have two labeled angles: one is \( 2x^\circ \) and the other is \( 3x^\circ \). These two angles appear to form a linear pair because their sum is a straight line, which measures \( 180^\circ \).

### Step-by-step solution:

1. **Equation for angle sum:**
   Since angles \( \angle ABD \) (measuring \( 2x^\circ \)) and \( \angle DBC \) (measuring \( 3x^\circ \)) form a straight line, the sum of these two angles should equal \( 180^\circ \). So, the equation is:
   \[
   2x + 3x = 180
   \]

2. **Solving for \( x \):**
   \[
   5x = 180
   \]
   \[
   x = \frac{180}{5} = 36
   \]

3. **Measure of \( \angle ABD \):**
   Since \( \angle ABD = 2x \):
   \[
   \angle ABD = 2(36) = 72^\circ
   \]

4. **Measure of \( \angle DBC \):**
   Since \( \angle DBC = 3x \):
   \[
   \angle DBC = 3(36) = 108^\circ
   \]

### Answers:

- Equation: \( 2x + 3x = 180 \)
- \( x = 36 \)
- \( m \angle ABD = 72^\circ \)
- \( m \angle DBC = 108^\circ \)

Would you like further explanation on any step, or have any additional questions? Here are 5 related questions that might help deepen understanding:

1. What are the characteristics of a linear pair of angles?
2. How do you verify that two angles form a straight line?
3. Can two angles have different measures but still add up to \( 180^\circ \)?
4. How do complementary angles differ from supplementary angles?
5. If one of the angles were \( 4x \) instead of \( 3x \), how would the solution change?

**Tip:** For any angles that form a straight line, their sum will always be \( 180^\circ \).

Given the angles in the image, find the equation and the measures of angles ABD and DBC.

Learn how to solve a linear pair angle problem with angles ABD and DBC. Using the equation 2x + 3x = 180, we find that x = 36. This means angle ABD measures 72° and angle DBC measures 108°. Ideal for students in Grades 6-8 studying geometry and angle relationships.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation