The sum of all angles of atriangle is equals 180degree.Explain?

Answer 1

The best way is to start with a square. Every angle in a square is 90. if you add them up, you get 360 degrees. A triangle can be made by making a diagonal in the square. Since it is a square, the opposite angles are bisected, so you have one 90 degree angle, and 2 - 45 degree angles. Add them up: 90 + 45 + 45 = 180. Move on to a rectangle. Same 4 90 degree angles. Make a diagonal. Since the opposite sides of a rectangle are parallel, the diagonal creates opposite interior angles, which are congruent. The two angles created by the diagonal on each corner also add to 90. Thus, inside your triangle, you have the right angle, one angle a, and the other is the complimentary angle 90 - a. Add these up and you get 90 + a + (90 - a) = 90 + 90 + a - a = 90 + 90 = 180. Using this logic, it is similar for a parallelogram (which defines all triangles), and now you have all angles of a triangle sum to 180 degrees. If this is confusing, just go with it.