Angles can be found all around us, from the shape of a triangle to the arc of a rainbow. They are important in mathematics and geometry, but what exactly is an angle and what is the undefined term used to define it?
What is an Angle?
An angle is a figure or shape formed between two lines or planes that meet at a point. It is measured in degrees and is a measure of the amount of turn between the two lines or planes. Angles can be either acute, obtuse, right, straight, reflex or full. Acute angles are less than 90 degrees, obtuse angles are greater than 90 degrees and less than 180 degrees, right angles are equal to 90 degrees, straight angles are equal to 180 degrees, reflex angles are greater than 180 degrees and less than 360 degrees, and full angles are equal to 360 degrees.
What is the Undefined Term Used to Define an Angle?
The undefined term used to define an angle is the vertex. The vertex of an angle is the point where the two lines or planes meet. It is also sometimes referred to as the apex or the corner of the angle. The vertex of an angle can also be used to determine the angles' measure, as the angle is measured from the vertex.
How to Label Angles
Angles can be labeled in two ways. The most common way is to label them with the vertex and the angle's measure. For example, an angle labeled "A" with a measure of 90 degrees would be written as ∠A = 90°. The other way to label an angle is with three points. For example, an angle formed by points A, B, and C would be written as ∠ABC.
What is an Angle Bisector?
An angle bisector is a line or a ray that divides an angle into two equal parts. The angle bisector passes through the vertex of the angle and can be used to determine the measure of an angle. For example, an angle bisector that divides an angle into two 45 degree angles would create a 90 degree angle.
What is an Exterior Angle?
An exterior angle is an angle formed outside of a triangle or other polygon. It is formed by extending one of the sides of the triangle or polygon and then measuring the angle formed between the extended side and the adjacent side. The measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles.
What is the Angle Addition Postulate?
The angle addition postulate states that if two angles form a linear pair, then the measure of the angles added together is equal to the measure of the third angle in the pair. This postulate can be used to solve for the measure of an unknown angle.
What is an Angle Pair?
An angle pair is two angles that are next to each other and share a common vertex and side. Angle pairs can be either adjacent angles, which are angles that have a common vertex and a common side, or vertical angles, which have the same measure but do not share a common side.
What is a Protractor?
A protractor is a tool used to measure angles. It is usually a semi-circle with a handle at the center and degrees marked off along the edge. It is used by placing the center of the protractor at the vertex of the angle and then lining up the zero-degree mark with one of the sides of the angle. The degrees can then be read off the protractor to determine the measure of the angle.
Conclusion
The undefined term used to define an angle is the vertex. The vertex is the point at which two lines or planes meet to form an angle. Angles can be labeled with the vertex and the angle's measure, with three points, or with an angle bisector. Exterior angles are angles formed outside of a triangle or polygon, and the angle addition postulate can be used to solve for the measure of an unknown angle. Angle pairs are two angles next to each other and sharing a common vertex and side, and a protractor is a tool used to measure angles.
