Table of Contents
Angle Definition
An angle is a figure formed by two rays, called the sides of the angle, that meet at a point called the vertex. The angle is measured in degrees, with 360 degrees making a full circle. An angle can also be measured in radians, with 2π (or 6.283185307179586) radians making a full circle.
Acute Angle
An acute angle is an angle that is less than 90 degrees.
Right Angle Triangle
A right angle triangle is a three-sided figure in which one of the angles is a right angle. The other two angles are acute angles.
Obtuse Angle
An angle that is greater than 90 degrees and less than 180 degrees is called an obtuse angle.
Straight Angle
A straight angle is an angle with a measure of 180 degrees.
Reflex Angle
The reflex angle is the angle formed between two lines that are perpendicular to each other. The reflex angle is also known as the right angle.
Complementary Angles
Two angles are complementary if their sum is 90 degrees.
For example, if angle A is complementary to angle B, then angle A + angle B = 90 degrees.
Supplementary Angles
A supplementary angle is an angle that is adjacent to a right angle, and its measure is the sum of the measures of the two adjacent angles.
Relationships Between Angles
Angles are related to each other based on either their summation or where they lie on two intersecting lines:
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Complementary Angles
Two angles are called complementary angles to each other if they sum up to 90 degrees. It is not necessary for the angles to be adjacent to each other to be called complementary angles. As long as their summation is 90 degrees, they are termed complementary angles. In the diagram below, both sets of angles are complementary. In the first one, they are adjacent to each other while in the second one they are not.
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Supplementary Angles
supp. angles are angles whose sum is 180 degrees. Supplementary angles could be of different types as described below:
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Vertical angles – When two lines cross, the angles opposite to each other are called vertical angles. vertical angles are equal in measure. In the figure below, angles 1 and 3 are vertical angles and equal to each other. Angles 2 and 4 also form vertical angles and are equal to each other.
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Alternate interior angles – When we draw a traversal to two straight lines, the angles on the opposite sides of the traversal that lie on the interior side constitute the alternate interior angles If the two lines are parallel to each other, then alternate interior lines are equal. Angles 2 and 3 are alternate interior angles in the image below.
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Alternate exterior angles – When we draw a traversal to two straight lines, the angles on the opposite sides of the traversal that lie on the exterior side constitute the alternate exterior angles. If the two lines are parallel to each other, then alternate exterior lines are equal. Angles 1 and 4 are alternate exterior angles here.
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Corresponding angles – When a line crosses two lines, the angles in matching corners are called corresponding angles. One of them is internal, and another is external. Corresponding angles are equal if the two lines (which are intersected) are parallel to each other. In the image below angles, 1 and 2 are corresponding angles . Here 1 is the external angle, and 2 is the internal angle.
