from a handpicked tutor in LIVE 1-to-1 classes
A complete angle is a type of angle that measures 360°. An angle is formed when two lines intersect at a point and the measure of the opening between these two lines. There are different types of angles such as a right angle, acute angle, obtuse angle, and so on. A complete angle deals with one full rotation measuring 360°. Let us learn more about this interesting concept of complete angles and solve a few examples.
|1.||Definition of Complete Angle|
|2.||Representing Complete Angle|
|3.||Forming a Complete Angle|
|4.||FAQs on Complete Angle|
Definition of Complete Angle
If after one whole rotation, the final ray coincides with the incident or initial ray, then the angle so formed is known as the complete angle. The other names are a full angle and a round angle. The angle is equal to 2π radians = 360 degrees corresponding to the central angle of an entire circle. Four right angles or two straight angles make a complete angle. The angle is similar to a zero angle but the difference is the amount of rotation.
Representing Complete Angle
A complete angle can be represented in three different angle measuring systems, they are:
- A complete angle is represented as 360° in the sexagesimal system.
- A complete angle is represented as 2π in a circular system.
- A complete angle is represented as 400g in the centesimal system.
Forming Complete Angle
A complete angle can be formed in two ways, they are:
Complete Angle by a Line
Consider a ray AD that is placed at a plane. When the ray AD is rotated to an angle of 360° to reach the same position, another ray AC is created. The angle made by the ray to reach its final position from its initial position is ∠CAD and the amount of rotation required is 360°. Therefore, ∠CAD = 360° and is a complete angle.
Complete Angle Between Two Lines
Consider two rays PQ and PR, the two rays make the same angle, however, the angle between the two rays makes a complete angle. The angle between the two rays is written as ∠RPQ = 360° since it completes a full rotation.
Listed below are a few interesting topics related to complete angles, take a look.
Complete Angles Examples
Example 1: Sam goes for a morning run around a rectangular park starting from point A and ending at point A. In a single round, he covers 4 right angles. Determine the degree.
Solution: Since Sam completes an entire round starting from point A and ending at the same point with covering 4 right angles, he completes an angle. That means, the degree covered by Sam is 360° making it a full angle.
Example 2: Bella tries to walk around a square block from section D to reach back at the same starting point. But she stops halfway through at section F. Can you determine the degree and angle that she covers?
Solution: To complete a round starting from section D and back at section D, Bella needs to complete the full rotation. This means she needs to complete a full angle covering 360°. Since she stops halfway, she is only able to cover half the distance i.e. she stops at 180°. Hence making it a straight angle.
Practice Questions on Complete Angles
FAQs on Complete Angles
What is a Complete Angle?
When an angle completes its full rotation starting from 0 degrees and ends at 360 degrees it is known as a complete angle, Its measurement is equal to 360 degrees.
What are the 6 Types of Angles?
The 6 types of angles are right angles, acute angles, obtuse angles, straight angles, reflex angles, and complete angles.
What is the Full or Complete Angle?
An angle that completes a full rotation i.e. 1 complete turn with starting and ending at the same point is called a complete or full angle. The degree of a complete angle is 360° or 2π.
How Does a Complete Angle Look?
A complete angle covers the entire rotation starting and ending at the same point. It is a full circle with a rotation of 360°.
What is the Difference Between Complete Angle and Reflex Angle?
A complete angle is a full circle with a rotation of 360°. Whereas a reflex angle is a type of angle that measures more than 180° but less than 360°. For example, 192°, 250°, 178°, etc are all reflex angles.
How Do You Make a Complete Angle?
A complete angle can be made with two methods, first by using lines and second by using two lines. A line can construct a complete angle with the help of a ray that completes a full rotation of 360° with the ray being constant of a plane. Constructing a complete angle between two lines is done by again using two rays on the same plane with the same points that complete a full rotation.