Question

Two acute angles whose sum is a right angle are called _____ angles.

Short answer

Complementary angles.

Step-by-step solution

Understand the Definitions

Acute angles are angles that are less than 90 degrees. A right angle is an angle that is exactly 90 degrees.

Recognize the Relationship

The problem states that the sum of two acute angles equals a right angle. We need to determine the name for such a pair.

Recall the Term

Angles whose measures add up to 90 degrees are known as complementary angles. Since the sum of the two acute angles is a right angle, these angles are complementary.

Key concepts

Acute Angles

In geometry, an angle is classified based on its measure in degrees. Acute angles are a specific type of angle that measure less than 90 degrees. These angles are often found in various shapes and are common in triangles, especially in equilateral and isosceles triangles. Understanding acute angles helps in identifying and working with different types of geometric figures.
An acute angle looks small and its vertex forms a sharp point. Despite being small, acute angles play a crucial role in determining the shape and properties of geometric figures. For example, in a triangle with all acute angles, known as an acute triangle, each of the three interior angles is less than 90 degrees.

• They are always less than 90 degrees.
• They can be added together to form various other types of angles, including right and obtuse angles.
• They are commonly found in various geometric shapes and figures.

Right Angle

A right angle is an angle that measures exactly 90 degrees. It is one of the most fundamental angles in geometry and is easily recognizable due to its 'L' shape. Right angles are ubiquitous in everyday life, forming the basis of many architectural structures, furniture designs, and more.
A right angle is often represented in diagrams with a small square at the vertex of the angle, indicating that the angle is exactly 90 degrees. This square is used universally to denote that the angle is not acute (less than 90 degrees) or obtuse (more than 90 degrees).

• It measures exactly 90 degrees.
• Right angles are found in right triangles, rectangles, and squares.
• They are crucial for constructing perpendicular lines and ensuring proper alignment in various designs.

Angle Relationships

Understanding angle relationships is key in solving many geometric problems. One fundamental relationship is between complementary angles. Complementary angles are two angles whose measures add up to 90 degrees. This relationship is essential when working with various geometric configurations and proofs.
For instance, if we have two acute angles, say 30 degrees and 60 degrees, their sum is a right angle (30 + 60 = 90). These two angles are complementary. This concept can often be visualized through simple geometric shapes and real-life examples.

• Complementary angles add up to 90 degrees.
• They are often used to solve problems in geometry, such as finding the unknown angle in a right triangle.
• Other important angle relationships include supplementary angles (sum to 180 degrees) and adjacent angles (share a common side).