Two angles whose measures add up to exactly 90 degrees are called what type of angles?

Introduction / Context:
This geometry vocabulary question asks for the special name given to two angles whose measures sum to 90 degrees. Knowing names for pairs of angles is important in geometry because these relationships often appear in problems involving triangles, parallel lines and right angles. The focus here is on the pair that forms a right angle when combined.

Given Data / Assumptions:

• There are two angles being considered.
• The sum of their measures is exactly 90 degrees.
• We are asked for the standard geometric term used for such a pair of angles.
• The available answer choices include several different types of angle relationships.
• We assume standard terminology used in school level Euclidean geometry.

Concept / Approach:
There are two key words that often cause confusion: complementary and supplementary. Complementary angles are two angles whose measures add up to 90 degrees, while supplementary angles are two angles whose measures add up to 180 degrees. The other terms in the options, such as corresponding and alternate angles, describe positional relationships when lines are cut by a transversal, not simple sums of measures. Therefore the correct answer must match the 90 degree sum, which is complementary.

Step-by-Step Solution:
Step 1: Recall the definition of complementary angles: two angles are complementary if the sum of their measures is 90 degrees.Step 2: Recall the definition of supplementary angles: two angles are supplementary if the sum of their measures is 180 degrees.Step 3: Compare the condition in the question with these definitions. The question states that the two angles have a sum of 90 degrees.Step 4: This matches exactly the definition of complementary angles.Step 5: Therefore the correct classification is complementary angles.

Verification / Alternative check:
We can use a simple numeric example. Suppose one angle measures 30 degrees and the other measures 60 degrees. Together they sum to 30 + 60 = 90 degrees. This is a classic example of complementary angles. In contrast, a pair of 100 degrees and 80 degrees would sum to 180 degrees and be called supplementary angles. This comparison confirms that the 90 degree sum corresponds to complementary, not supplementary.

Why Other Options Are Wrong:
Supplementary angles, listed in option a, have a sum of 180 degrees, not 90 degrees. Corresponding angles, in option b, are formed when a transversal cuts two lines and refer to matching positions, not to a particular sum. Alternate angles, in option d, also describe positions relative to a transversal and lines, such as alternate interior angles, again not a specific total measure. None of these match the condition of adding up to 90 degrees.

Common Pitfalls:
A very common memory mistake is confusing complementary with supplementary, especially because both words sound somewhat similar. A helpful trick is to associate the letter C in complementary with the number 90 by thinking of a right angle corner. Another idea is to remember that S in supplementary can be linked with straight angle, which has 180 degrees.

Final Answer:
Two angles whose measures add up to 90 degrees are called Complementary angles.