the sum of the measures of angles ∠dbe and ∠ebc is 180°, so they are also called what kind of angles?
supplementary angles
vertical angles
linear pair
complementary angles

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# Brief Explanations:
1. Recall the definitions:
   - Supplementary angles: Two angles whose sum is $180^\circ$.
   - Vertical angles: Opposite angles formed by the intersection of two lines, they are equal.
   - Linear pair: A pair of adjacent angles that form a straight line (sum to $180^\circ$) and are adjacent (share a common side and vertex). But the question here is about the name for two angles with a sum of $180^\circ$ in general. Wait, but looking at the diagram, $\angle DBE$ and $\angle EBC$ – wait, maybe I misread. Wait, the sum is $180^\circ$. But let's check the options again. Wait, the first option is supplementary angles (sum to $180^\circ$), linear pair is a type of supplementary angles that are adjacent. But the question says "the sum of the measures... is $180^\circ$, so they are also called what kind of angles?" So the general term for two angles with sum $180^\circ$ is supplementary angles. Wait, but maybe the diagram shows they are adjacent? Wait, the diagram has point B, with BE as a ray, and D and C on either side? Wait, maybe I made a mistake. Wait, no: supplementary angles are two angles whose measures add up to $180^\circ$. Linear pair is a specific case of supplementary angles where they are adjacent (form a straight line). But the question is asking for the kind of angles when their sum is $180^\circ$. So the answer should be supplementary angles? Wait, no, wait the options: linear pair is also a candidate. Wait, let's re - examine the definitions:

- Supplementary angles: Any two angles (adjacent or not) with a sum of $180^\circ$.
   - Linear pair: Two adjacent angles that form a straight line (so their non - common sides form a straight line), and their sum is $180^\circ$.

But the question says "the sum of the measures of angles $\angle DBE$ and $\angle EBC$ is $180^\circ$". If we look at the diagram (from the given image, B is a point, with a horizontal line AF, and a vertical line BE, and points D and C). So $\angle DBE$ and $\angle EBC$ – wait, maybe they are adjacent? Wait, no, maybe the correct term is supplementary angles. Wait, no, the linear pair: a linear pair of angles is formed when two lines intersect. But in this case, if $\angle DBE$ and $\angle EBC$ are adjacent and form a straight line (sum to $180^\circ$), but the question is about the name for two angles with sum $180^\circ$. Wait, the first option is supplementary angles. Wait, but let's check the options again:

- Supplementary angles: Sum to $180^\circ$.
   - Vertical angles: Equal, formed by intersecting lines.
   - Linear pair: Adjacent supplementary angles.
   - Complementary angles: Sum to $90^\circ$.

Since the sum is $180^\circ$, the angles are supplementary angles. But wait, maybe the diagram shows they are a linear pair? Wait, the diagram has B as a vertex, with BE as a ray, and D and C such that $\angle DBE$ and $\angle EBC$ are adjacent and form a straight line? Wait, no, maybe I am overcomplicating. The key is that two angles with a sum of $180^\circ$ are called supplementary angles. But wait, the option "linear pair" is also a type of supplementary angles. But the question is phrased as "the sum of the measures... is $180^\circ$, so they are also called what kind of angles?" So the general term is supplementary angles. Wait, no, maybe the answer is linear pair. Wait, let's think again. A linear pair is two adjacent angles that form a straight line (so their sum is $180^\circ$). If the two angles $\angle DBE$ and $\angle EBC$ are adjacent (share the side BE and the vertex B) and their non - common sides form a straight line (so that their sum is $180^\circ$), then they are a linear pair. But the question says "the sum of the measures... is $180^\circ$", so the answer should be supplementary angles? Wait, no, the difference between supplementary angles and linear pair: supplementary angles can be non - adjacent, linear pair are adjacent. But in the diagram, since there is a right angle at B (the square), and the horizontal line AF, and vertical line BE, maybe $\angle DBE$ and $\angle EBC$ are adjacent and form a straight line? Wait, maybe the correct answer is supplementary angles. Wait, no, let's check the definitions again.

Supplementary angles: Two angles whose measures add up to $180^\circ$.

Linear pair: A pair of adjacent angles that form a straight line (so their sum is $180^\circ$).

So if the sum is $180^\circ$, the general term is supplementary angles. But maybe the diagram shows they are adjacent, so linear pair? Wait, the options are: supplementary angles, vertical angles, linear pair, complementary angles.

Vertical angles are equal, so not. Complementary sum to $90^\circ$, so not. So between supplementary and linear pair.

Wait, the question is "the sum of the measures... is $180^\circ$, so they are also called what kind of angles?" So the answer is supplementary angles? But maybe the diagram shows they are a linear pair. Wait, maybe I made a mistake. Let's see: in the diagram, point B, with a horizontal line (AF) and a vertical line (BE), and points D and C. So $\angle DBE$ and $\angle EBC$ – if D is above and C is below, then $\angle DBE$ and $\angle EBC$ are adjacent and form a straight line (a straight angle), so they are a linear pair. But the sum of a linear pair is $180^\circ$, and linear pair is a specific type of supplementary angles. But the question is asking for the name of angles with sum $180^\circ$. Wait, the term for two angles with sum $180^\circ$ is supplementary angles. But the option "linear pair" is also correct in the sense that a linear pair is supplementary. But which is more appropriate?

Wait, let's check the definitions again:

- Supplementary angles: Two angles whose measures add up to $180^\circ$. They don't have to be adjacent.

- Linear pair: Two adjacent angles that form a straight line (so their non - common sides are opposite rays), and their sum is $180^\circ$.

Since the question is about the sum being $180^\circ$, the answer should be supplementary angles? But maybe the diagram shows they are adjacent, so linear pair. Wait, the diagram has a right angle at B (the square), so BE is perpendicular to AF. Then $\angle EBC$ and $\angle DBE$ – if D is on one side and C on the other, maybe they are adjacent. Wait, I think the correct answer is supplementary angles. Wait, no, the linear pair is a pair of adjacent supplementary angles. But the question is "the sum of the measures... is $180^\circ$, so they are also called what kind of angles?" So the answer is supplementary angles. But let's check the options again. The first option is supplementary angles. So I think the answer is supplementary angles.
# Answer:
supplementary angles

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