Question

The sum of all the three angle is a triangle is:

Answer 1

Hint: In a Euclidean space the sum of angles of a triangle equals the straight angle. A triangle has three angles, one at each vertex, bounded by a pair of adjacent sides. It was unknown for a long time whether other geometries exist for which sum is different.
Triangle: - A triangle is a polygon with three edges c and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B and C is denoted.
Area\[ = \dfrac{1}{2} \times Base \times Height\]
perimeter\[ = \] Sum of side length of triangle.
No. of vertices \[ = 3\]
No. of edges\[ = 3\]
Internal angle\[ = 60\]
Properties are convex, cyclic, equilateral isogonal, and isotoxal.

Complete step-by-step solution:
ABC is a triangle
Through point A draw a line
\[ \Rightarrow \angle ABC = \angle EAB\] (Alternate Angles)
Here, we are comparing the angles
\[ \Rightarrow \angle EAb + \angle BAC + \angle FAc = {180^0}\](Linear pair)
By Substituting \[ \Rightarrow \angle EAb = \angle ABC\,and\angle BAC = \angle BCA\]
\[\angle ABC + \angle CAB + \angle ACB = 180\]
The sum of all the three angles in a triangle is \[{180^0}\]

Note:In the other words the other two angles in the triangle (the ones that add up to form the interior angle) must combine with the angle in the bottom right corner to make the \[180\] degree angle. The interior angle of the triangle. Must always add up to \[{180^0}\]\[EFII BC\]