The figure shows adjacent angles BAC and CAD, which are two angles that share a common side and vertex. Adjacent angles are commonly encountered in geometry and have several interesting properties and applications.
In this article, we will explore the definitions, properties, and applications of adjacent angles. We will also provide a step-by-step guide for measuring adjacent angles using a protractor.
Definitions and Concepts
Adjacent angles are two angles that share a common side and a common vertex. In other words, they are angles that lie side-by-side, with no other angles in between.
The figure below illustrates adjacent angles BAC and CAD. Angle BAC is formed by rays BA and AC, while angle CAD is formed by rays CA and AD. The common side is AC, and the common vertex is A.
Adjacent angles have a special relationship. The sum of the measures of two adjacent angles is always 180 degrees.
Properties of Adjacent Angles
The theorem that states the sum of adjacent angles is 180 degrees is known as the Adjacent Angles Theorem.
Here are some examples of adjacent angles that add up to 180 degrees:
- A 90-degree angle and a 90-degree angle
- A 60-degree angle and a 120-degree angle
- A 45-degree angle and a 135-degree angle
The converse of the Adjacent Angles Theorem is also true. If the sum of the measures of two angles is 180 degrees, then the angles are adjacent.
Measuring Adjacent Angles, The figure shows adjacent angles bac and cad
Adjacent angles can be measured using a protractor.
To measure adjacent angles using a protractor, follow these steps:
- Place the center of the protractor on the vertex of the angles.
- Align the 0-degree mark of the protractor with one of the rays that form the angles.
- Read the measure of the angle on the protractor.
- Repeat steps 2 and 3 for the other angle.
Applications of Adjacent Angles
Adjacent angles are used in a variety of real-world applications, including architecture, engineering, and design.
For example, adjacent angles are used to:
- Design buildings and other structures
- Create blueprints and other technical drawings
- Solve geometry problems
Answers to Common Questions: The Figure Shows Adjacent Angles Bac And Cad
What is the sum of adjacent angles?
The sum of adjacent angles is always 180 degrees.
How do you measure adjacent angles using a protractor?
To measure adjacent angles using a protractor, place the center of the protractor on the vertex of the angles. Align the 0-degree mark of the protractor with one of the sides of the angles. Read the measurement of the other side of the angles on the protractor.
What are some real-world applications of adjacent angles?
Adjacent angles are used in architecture to design buildings and bridges. They are also used in engineering to design machines and structures. In addition, adjacent angles are used in design to create patterns and shapes.
