The problem states that a worker is cutting a ceramic tile in the shape of a triangle, where the sum of two of the triangle’s angles equals $80^\circ$. We are asked to identify the type of triangle formed.

To solve this, we can recall that the sum of the interior angles of any triangle is always $180^\circ$. Given that the sum of two angles is $80^\circ$, we can find the measure of the third angle as follows:

$180^\circ - 80^\circ = 100^\circ$

This implies that the triangle has one angle measuring $100^\circ$ and two other angles that sum to $80^\circ$. Therefore, this triangle must have an angle greater than $90^\circ$, making it an obtuse triangle.

Answer:

The triangle that composes this ceramic tile is an obtuse triangle.

Would you like further details on the solution, or do you have any questions?

Here are some related questions to deepen your understanding:

1. What are the properties of an obtuse triangle?
2. How does knowing the sum of angles in a triangle help in geometry problems?
3. Can a triangle have more than one obtuse angle?
4. What other types of triangles can be classified by their angles?
5. How would the problem change if the sum of two angles was different, like $90^\circ$?

Tip: In triangle problems, remember that the sum of the interior angles is always $180^\circ$.