Welcome to our lesson on angles in 7th-grade math. An angle is formed when two rays share a common endpoint called the vertex. The measure of an angle is the amount of rotation between these two rays. We use the Greek letter theta to represent the angle measure. The two rays form the sides of the angle, and the point where they meet is called the vertex.
Angles are classified into different types based on their measure. An acute angle measures less than 90 degrees, like this 45-degree angle. A right angle is exactly 90 degrees, forming a perfect corner. An obtuse angle measures more than 90 degrees but less than 180 degrees, such as this 135-degree angle. Finally, a straight angle measures exactly 180 degrees, forming a straight line. Understanding these angle types is essential for geometry and many real-world applications.
To measure an angle, we use a tool called a protractor. First, place the center of the protractor at the vertex of the angle. Next, align the zero-degree line of the protractor with one ray of the angle. Then, look where the second ray intersects the protractor's scale and read the degree measurement. In this example, we can see that our angle measures 60 degrees. Protractors typically have two scales, so make sure you're reading from the correct one based on how you aligned the protractor.
In geometry, we study several important angle relationships. Adjacent angles share a common vertex and side, but don't overlap. Vertical angles are formed when two lines intersect. These opposite angles, like alpha here, are always equal in measure. Complementary angles are two angles whose measures add up to 90 degrees, like these 30-degree and 60-degree angles. Supplementary angles are two angles whose measures add up to 180 degrees, such as these 135-degree and 45-degree angles. Understanding these relationships helps us solve problems involving unknown angle measures.
To summarize what we've learned about angles: An angle is formed by two rays that share a common vertex. We classify angles based on their measure as acute, right, obtuse, or straight. We use a protractor to measure angles in degrees. Important angle relationships include vertical angles which are equal, complementary angles that sum to 90 degrees, and supplementary angles that sum to 180 degrees. Understanding these angle concepts and relationships is essential for solving geometric problems and is the foundation for more advanced mathematics.