https://file.aiquickdraw.com/mathbot/file/17255851507805tzg8ugt.jpg

I can help solve the problem from the image. Let's start by analyzing the content.

The image shows two angles, ∠DBE and ∠EBC, which are **supplementary** (they add up to 180°). The angle measures are:

- \( \angle DBE = 6x + 19^\circ \)
- \( \angle EBC = 3x + 20^\circ \)

We know that supplementary angles add up to 180°, so the equation to solve is:

\[
(6x + 19^\circ) + (3x + 20^\circ) = 180^\circ
\]

Let me solve this equation for \( x \).The value of \( x \) is \( \frac{47}{3} \), or approximately \( 15.67 \).

Now, let's substitute this value back into the expressions for \( \angle DBE \) and \( \angle EBC \) to find their actual measures. I'll calculate that next.The measures of the two angles are:

- \( \angle DBE = 113^\circ \)
- \( \angle EBC = 67^\circ \)

These two angles add up to \( 180^\circ \), confirming that they are supplementary.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. What are complementary angles, and how do they differ from supplementary angles?
2. How can you determine if two angles are adjacent or non-adjacent?
3. What is the sum of the interior angles in any triangle?
4. Can supplementary angles ever be congruent?
5. How do you solve for unknown angles in a polygon?

**Tip:** Always check if angles are complementary or supplementary based on their sum (90° for complementary and 180° for supplementary).

Given that ∠DBE and ∠EBC are supplementary angles, find ∠DBE and ∠EBC where ∠DBE = 6x + 19° and ∠EBC = 3x + 20°.

Learn how to solve for ∠DBE and ∠EBC given that they are supplementary angles. The problem involves solving a linear equation and substituting the value of x back into the expressions for the angles.

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