Angles and Sides in Geometry
- Written by: NewsServices.com
From our previous stints in the topic of geometry, we know different terms such as angle, sides, etc. Angle is the measure of separation between two sides of a geometrical figure or to say more generically it is the measure of separation between two lines. There are different types of angles. Some of which are listed below:
Acute angle: The angles which measure less than 90° are called acute angles. They have their measure anywhere in the range of 0° to 90°, excluding these two measures.
Right angle: The angles which measure exactly equal to 90° are called right angles. If a line is perpendicular on any surface or to any other line then it is said to form a right angle with that surface or line.
Obtuse angle: The angles which measure more than 90° are called obtuse angles. They have their measure in the bracket of (90°, 180°), excluding these two measures.
Straight angle: It is an angle which has its measure exactly equal to 180°. This angle is also referred to as a combination of the acute angle and the obtuse angle.
Supplementary angle: Angles which have their sum is equal to 180° are called supplementary angles. There are various kinds of supplementary angles too which we shall learn later in here.
Complementary angle: Angles which have their sum is equal to 90° are called complementary angles. There are various kinds of complementary angles too which we shall learn later in here.
Reflex angle: Angles which are in the range of 180° to 360° are known as reflex angles. The thing to be noted here is that for an angle to be called reflex angle it should measure more than 180° and less than 360° and not equal to these measures under any circumstances.
Vertically opposite angles: In the above given figure what we are seeing is a line intersecting two parallel lines. This leads to the formation of a number of angles.
Angles denoted by the numbers (2,3), (1,4), (6,7) & (5,8) are vertically opposite angles. As they are opposite to each other on a vertical line.
Corresponding angles: In the above given figure what we are seeing is a line intersecting two parallel lines. This leads to the formation of a number of angles. Angles denoted by the numbers (2,6) & (1,5) are corresponding angles.
Interior alternate angles: In the above given figure what we are seeing is a line intersecting two parallel lines. This leads to the formation of a number of angles. Angles denoted by the numbers (3,6) & (4,5) are interior alternate angles.
Exterior alternate angles: In the above given figure what we are seeing is a line intersecting two parallel lines. This leads to the formation of a number of angles. Angles denoted by the numbers (1,8) & (2,7) are exterior alternate angles.
Association with triangles:
There is a great deal of association of angles with triangles. It is rampant to such an extent such that a number of triangles are named after the angles present in them. Let us see some of those types of triangles:
Acute triangle: In acute triangle all the angles that are present within it have their measure less than 90°. Sum of all three angles of this type of triangle is equal to 180°.
Obtuse triangle: In an obtuse triangle one of the angles measures more than 90° while the remaining two have their respective measures less than 90°. Sum of all three angles of this type of triangle is equal to 180°.
Right triangle: In the right triangle one of the angles exactly measures 90° while the other two measure less than 90° each. Sum of all three angles of this type of triangle is equal to 180°.
Conclusion:
Careful examination of the facts and details mentioned above regarding angles fetches us a lot of interesting insights. It also lets us know about the different types of angles, their properties etc. Additionally, we also came to know about a number of triangles which are named after angles and their respective property. If you intend to learn more about angles and its different types, you can visit Cuemath.
