An angle is a shape formed when two straight lines or rays meet at a point called vertex. The lines or rays that form the angle are referred to as arms of the angle. Angles are used to measure things like the corners of shapes, the direction something is pointing, and how things are positioned in space.
The types of angles are based on the values of angles in degrees. There are six main types of angles, they are:
An acute angle is less than 90 degrees, meaning it is "sharp" or "narrow".
In other words, it falls between 0 and 90 degrees. The image given above shows an example of an acute angle.
An obtuse angle is greater than 90 degrees but less than 180 degrees, meaning it is "blunt" or "wide". It is the opposite of an acute angle. When two lines intersect and form an angle that is wider than 90 degrees, it is referred to as an obtuse angle. The given figure represents an obtuse angle.
A right angle is exactly 90 degrees, and is often marked by a square in diagrams. The image below depicts an example of a right angle.
A straight angle is exactly 180 degrees, meaning it forms a straight line.
A reflex angle is greater than 180 degrees but less than 360 degrees. The figure below shows an example of a reflex angle.
An angle that measures 360 degrees is referred to as a full rotation or full angle. This occurs when one of the arms completes a full rotation to form the angle.
Type of angles | Angles |
Acute Angle | < 90° |
Obtuse Angle | > 90°, < 180° |
Right Angle | = 90° |
Straight Angle | =180° |
Reflex Angle | >180°, < 360° |
Zero Angle | =0° |
Full rotation/complete angle | =360° |
Angles are not just about their measurements, they can also be related to each other. Angle relationships are important in mathematics and can help us solve various problems. Understanding these relationships can give us insights into geometric shapes and their properties. In this paragraph, we will explore different angle relationships and their significance in mathematics.
Types of Angle Relationships
Interior angles are those that lie inside the polygon or a closed shape having sides and angles. Exterior angles are formed outside the shape, between any side and line extended from adjacent sides.
Adjacent angles are two angles that have a common vertex and a common side, but no common interior points. They are often found in geometric figures, such as polygons and triangles.
Vertical angles are pairs of angles opposite each other when two lines intersect. They have the same measure and are congruent.
Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then A + B = 90 degrees.
Supplementary angles are two angles that add up to 180 degrees. In other words, if one angle is x degrees, the other angle will be 180 - x degrees.
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