In basic geometry, two angles whose sum is 180 degrees are called what kind of angles?

Introduction / Context:
This question tests knowledge of standard terminology for angle relationships in geometry. Many questions in geometry, trigonometry, and coordinate geometry implicitly assume familiarity with terms like complementary, supplementary, and alternate angles. Knowing the definitions enables quick recognition of relationships and simplifies problem solving involving straight lines and right angles.

Given Data / Assumptions:
- We consider two angles whose measures add up to 180 degrees.
- These angles may be adjacent (forming a straight line) or separate, but their measures still sum to 180 degrees.
- We use conventional Euclidean geometry terminology.

Concept / Approach:
In geometry, two angles whose sum is 90 degrees are called complementary angles. Two angles whose sum is 180 degrees are called supplementary angles. Alternate angles are formed when a transversal intersects two lines and refer to relative positions, not necessarily to any particular sum. Vertical angles are formed by intersecting lines and are equal to each other, again without specifying any fixed sum. Therefore, we identify the correct name by matching the defining property: sum equals 180 degrees.

Step-by-Step Solution:
Step 1: Recall that complementary angles are defined as two angles whose measures add up to 90 degrees. Step 2: Recall that supplementary angles are defined as two angles whose measures add up to 180 degrees. Step 3: Alternate angles arise when a transversal cuts two lines and have positional descriptions such as alternate interior or alternate exterior; they are not defined by a fixed sum of 180 degrees. Step 4: Vertical angles are opposite angles formed when two straight lines intersect, and they are equal in measure, again not defined by sum 180 degrees. Step 5: Since the question states that the sum is 180 degrees, by definition these angles are supplementary angles.

Verification / Alternative check:
Consider a straight line. Any two adjacent angles forming a straight line sum to 180 degrees and are typically cited as examples of supplementary angles. For instance, angles of 110 degrees and 70 degrees sum to 180 degrees and are therefore supplementary. No other standard name is used for this specific sum, confirming that supplementary is the correct term.

Why Other Options Are Wrong:
Option Complementary angles: They sum to 90 degrees, not 180 degrees.
Option Alternate angles: This term describes relative positions with respect to a transversal and does not specify any fixed sum.
Option None of the above: Incorrect because the standard name supplementary angles exactly matches the given property.
Option Vertical angles: These are equal angles formed at the intersection of two lines, with no requirement that they sum to 180 degrees.

Common Pitfalls:
Students often confuse complementary and supplementary angles, mixing up which sum corresponds to 90 degrees and which to 180 degrees. A useful memory aid is that co in complementary goes with corner and right angles (90 degrees), while sup in supplementary can be linked with straight (180 degrees). Remembering this helps avoid mislabeling angle relationships.

Final Answer:
Two angles whose sum is 180 degrees are called supplementary angles.