Complete Angle specifically refers to a full rotation, measuring 360 degrees. In geometry, an angle is created when two lines meet at a point, and its measurement determines the opening between these lines. There are various types of angles, such as right angles, acute angles, and obtuse angles. Understanding this concept helps in dealing with angles that complete one full circular motion.
In this article, we will learn the types of angles, concepts of complete angles, construction and formation of complete angles, and real-life examples that look like complete angles.
What are Angles?
An angle is a geometric figure that represents the amount of rotation or deviation between two straight lines, rays, or line segments that meet at a common endpoint. The angle is denoted by the symbol “∠”. Let’s learn what are the different types of angles.
What is a Complete Angle?
A complete angle is like a full spin that measures 360°. It's all the way around in a circle. When lines cross, they create angles, and the complete angle shows the whole circle. People also call it a full angle or round angle. In math drawings, it looks like a curved line connecting two rays, making a circle.
The symbol 360° is used to show a complete angle that tells that it goes all the way around a point. This helps in geometry and math to talk about a full turn visually and with numbers. The image added below shows the complete angle.
Complete AngleDefinition of Complete Angle
A complete angle is an angle of measurement with 360°, it include a full rotation or circle around a point. The angle corresponding to central angle of circle is 360°
There are two ways to form a complete angle. One is by a line and other one is, between two lines. Let us understand both the ways of formation of a Complete angle
Complete Angle By a Line
When a ray or a lin; say AD is drawn on a plane, forms another ray, AC, after rotating 360 degrees. The angle created during this rotation, ∠CAD, makes a complete angle or angle of 360°.
This angle measures the amount of rotation needed for the ray to return to its original position. In simpler terms, when the ray AD makes a full circle, the angle ∠CAD formed during this process is considered a complete angle, measuring 360 degrees.
Complete Angle Between Two Lines
When two rays, PQ and PR, share the same angle, the angle between them forms a complete angle, denoted as ∠RPQ = 360°.
This signifies a full rotation around the point where the rays intersect. Despite the rays having the same angle, the complete angle measurement reflects the entire circular motion, illustrating a comprehensive angular perspective.
Construction of a Complete Angle
Complete angles are prepared using various methods that are,
- Using Compass
- Using Protector
Complete Angle using Compass
To draw a complete angle with a compass, begin by drawing a ray PQ. Position the compass pointer at endpoint P, adjust to a desired width, and place the pencil tip on ray PQ. Draw a circle, ensuring it intersects the initial point, creating a full rotation or complete angle.
Complete Angle using a Protector
To draw a complete angle, a round 360° protractor can be used. This tool that is shaped like a circle, simplifies the measurement and creation of angles in various applications. The image of a 360° protector is added below that is used to draw complete angles,
What is Measure of a Complete Angle?
A complete angle forms a full circle, and its measurement is considered to be 360°. This complete circle represents the completeness of possible angular direction around a point, commonly used in geometry and trigonometry to describe angles in a full rotation.
Examples of Complete Angle in Real Life
Some of the real life examples that looks like a complete angle are:
- Clock Hands: The movement of clock hands completing a full circle every 12 hours.
- Carousel Rides: The rotation of a carousel, with its circular motion.
- Ferris Wheel: The turning of a Ferris wheel throughout its cycle forms a complete angle that offer riders a panoramic view of the surroundings.
- Record Player: The rotation of a vinyl record on a record player completes a full circle.
Various examples of compete angles are shown in the image below,
What are Types of Angles?
Various Types of Angles, other than complete angles; on the basis of measure of the angles are,
- Acute Angle: An acute angle measures less than 90° and is often found in triangles and other geometric shapes.
- Right Angle: A right angle measures exactly 90°, forming an "L" shape commonly seen in squares, rectangles, and right-angled triangles.
- Obtuse Angle: An obtuse angle measures greater than 90° but less than 180°.An obtuse angle is commonly seen in various polygons.
- Straight Angle: A straight angle measures 180° that creates a straight line.
- Reflex Angle: A reflex angle measures more than 180° but less than 360° and are often encountered in circular sectors.
Types of AnglesApart from these angle there are other types of angles that are,
- Complementary Angles: Complementary angles add up to 90 degrees. These angles are frequently seen in right-angled triangles and complementary angle pairs.
- Supplementary Angles: Supplementary angles add up to 180 degrees and these are commonly found in linear pairs or adjacent angles.
- Vertical Angles: Vertical angles are opposite each other when two lines intersect that shares a common vertex; they are always equal in measure.
Read More,
Complete Angles Examples
Example 1: What is the measure of a complete angle formed by the minute hand on a clock after 45 minutes?
Solution:
Each minute on a clock corresponds to 6 degrees (360 degrees ÷ 60 minutes).
Multiply 6 degrees by the number of minutes (45 minutes).
6°×45 = 270°
Measure of Complete Angle after 45 minutes is 270°
Example 2: A record player completes 5 revolutions. What is the total measure of the angles formed during this rotation?
Solution:
Each revolution is a complete angle of 360 degrees.
Multiply the number of revolutions by the measure of a complete angle.
5 revolutions×360°/revolution=1800°
Total measure of the angles during 5 revolutions is 1800°
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