Measuring Angles Level 1 In the next series of videos we will learn how to measure angles, classify angles by size, name the parts of a grade and recognize congruent angles. In this video we will see how to name angles, We will then go over how to measure angles. In the previous videos we define an angle as a figure formed by two line segments or rays meeting at a common point called the vertex the plural would be vertices. The segments or rays that form the angle are known as the sides of the angle. Angles are named using the angle symbol. You can name an angle in a few ways we can use a vertex, we can use a point located on each ray or line segment and the vertex, or we can also use a single number. Another common way to name angles is by using Greek letters such as theta, alpha, or beta instead of numbers. For example the following angle can be indicated as angle SRT, or angle TRS or angle R or angle 1 of theta. The collection of all points between the sides of the corner is the inside of the corner.
Here the word interior is Latin for "inner". The inside of a corner is the area between the two rays or line segments that define it is the sides of the corner to form "jaws" that extend to infinity. The outside of a corner is the collection of all wise outside the corner, in other words the region on the plane that is not inland. Now that we have an overview of the basics of angles, let's talk about how we measure them. Just as a ruler is used to measure a line segment a protractor is a tool that is commonly used to measure angles. Angles are usually measured in terms of degrees, radial, gon, or nautical angles.
In this course we are using both grades the unit for measuring angles. You can think of the measure, or size, of an angle if the amount of your turn would do as you reach the apex, find together one side of the corner, and then turn to look along the other side of the corner. If you turn all the way up to face your starting direction you want to rotate 360 degrees, That means you turn in a full circle. We will cover the properties of circles in greater detail in a much later video, for now we will use a circle to visually represent the idea of turning around, that's why we use a circle as a symbol to indicate angles. We indicate angles using the degree symbol represented by a small stage circle floating above the right of the number Just like an exponent. Now that we know that if we turned in a full circle we would turn 360 degrees, the next thing to understand is the size of a single degree.
To get a sense of the size of a single grade, let's take a circle and cut it into 360 equal pieces using straight cuts that go through the center of the circle, by doing so this we end up with 360 individual angles and each angle or cut would measure 1 degree. Such a degree is equivalent to 1/360 of a complete revolution around the circle. Such a protractor is nothing more than half a circle broken up into 180 equal slices. A typical protractor will have two sets of numbers, the inner one starting at 0 degrees It is located on the lower right edge of the protractor and increases as you move counterclockwise around the protractor, the outer numbers start at 0 degrees which is located on the lower left side of the protractor and increase as you move clockwise around the protractor. We measure angles by placing the center mark of the protractor on the vertex of the angle and we align one radius (or segment) of the angle with the 0 degree mark on both sides, then the degree of the angle is given by the number falling on the other ray (or segment).
We usually use the inner numbers on the protractor for angles measured anticlockwise, and we use the outer numbers for angles measured clockwise. For example, the measurement of angle R is 30 degrees, similar to the measurement of a line segment; the measurement of an angle is indicated in a clear manner. In order to indicate the measurement of an angle We first write a lower case m followed by the name of the angle, it is read as "the measurement of angle R is 30 degrees". At times when the context is clear we can go ahead and indicate the measurement without write the lower case m, this is rarely done in most geometry textbooks. In these videos we will use the lower case m to indicate the measurement of an angle. If we have multiple angles that share the same vertex as the next figure we need use up to 3 letters to indicate each of the angles.
In this example angle ABC measures 60 degrees, this angle measure is equal to 1/6 of a revolution around a circle, angle ABD measures 90 degrees and it is equal to 1/4 of a revolution around a circle, angle ABE measures 120 degrees and is equal to 1/3 of a revolution around a circle, angle ABF measures 180 degrees and it is equal to 1/2 a revolution around a circle. Some math courses deal with negative angles, zero angles and angles greater than 180 degrees. In this course we will work with angles greater than 0 degrees and less than or equivalent to 180 degrees. When using a protractor it is not necessary to always adjust one of the sides of the corner with the 0 degree mark to measure the angle between 2 rays or 2 segments.
Similar to the way we measure a line segment using the coordinates of the endpoints, the degree of an angle is the absolute value of the difference of the degree measurement that the rays or segments correspond to on the protractor. For example, the measurement of angle EBC can be found by taking the absolute value of the difference between 120 degrees and 60 degrees or the absolute value of the difference between 60 degrees and 120 degrees. In this case, the measurement of angle EBC is 60 degrees. In general, the measure of an angle is the absolute difference of the real numbers that the rays or segments in accordance with the protractor. For example, if radius BA corresponds to the real number A and radius BC corresponds to the actual number C then the measurement of angle ABC will be equal to the absolute difference of a minus C or the absolute difference of C minus A. Well in our next video we will learn how to classify angles by sizes..