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Ever considered why the shape is called "Triangle"? Because this type of polygon contains three angles. These three angles might look pretty easy but don't fall for it. There is a lot of going on between these three angles. Let's see what kind of angular information we can get from a triangle.
In a triangle, there are two kinds of angles, interior angles and exterior angles.
The interior angles are formed on two sides, however, exterior angles are formed on one side and its extension. In the above diagram, are the exterior angles while points A, B, and C are the interior angles. Interior angles are denoted by red angle while exterior angles are denoted by the colour green. Both angles are interrelated to each other. If the interior angles increases, the exterior angle decreases and vice versa.
Properties of the Angles of a Triangle
There are three properties of the angles of a triangle. Let's discuss them.
1. The sum of the interior angles of a triangle equals .
2. The value of an exterior angle of a triangle equals the sum of the two nonadjacent interior angles.
3. The interior and exterior angles of a triangle at a particular vertex are supplementary, that is to say, they add up .
Types of Triangles by Angles
There are three types of triangles and these angles are categorized according to their angles.
Acute Triangle
An acute triangle has three acute angles. Acute angles mean angles that are less than .
Right Triangle
A right triangle has a right angle. You can figure it out by two straight horizontal and vertical lines coinciding with each other at a point. That point is where is formed. The longest side of this triangle is called the hypotenuse. The shorter sides of triangles are the legs or catheti (singular: cathetus). You might have heard base (adjacent) and perpendicular (opposite) instead of legs or cathetus.
Obtuse Triangle
An obtuse angle also has three angles but it has one angle that is an obtuse angle. Obtuse angle means an angle that is greater than .
I’m just curious if the area between the polygon and the circumscribed circle has a name.
https://www.superprof.co.uk/resources/academic/maths/geometry/plane/orthocenter-centroid-circumcenter-and-incenter-of-a-triangle.html