Make a triangle ABC

Draw a straight line through point A, and EF is parallel to BC.

Angle EAB= angle b

Angle FAC= angle c

Angle EAB+ Angle FAC+ Angle BAC = 180.

Angle BAC+ Angle B+ Angle C = 180.

2. The formula of the sum of internal angles (n-2) × 180.

3. Let three vertices of a triangle be A, B and C, corresponding to Angle A, Angle B and Angle C respectively; The straight line L passing through point A is parallel to the straight line BC, and the angle formed by L and ray AB is b', the angle formed by L and ray AC is c', and the angles b' and b, and c' and c respectively form internal angles. According to the equality theorem of internal angles of parallel lines, it can be concluded that the sum of internal angles of triangle = angle A+ angle B+ angle C= angle A+ angle B'+ angle C' = 65433.

4. extend the side ABC of the triangle, DAB = C+B, EBA = A+C, FCA = a+b.

So DAB+EBA+FCA = 2A+2B+2C = 360 (the sum of the outer angles of the triangle is 360).

So a+b+c = 180.

5. Extend one side of the triangle to form triangular diplomacy. It is easy to find that this angle and the inner angle of the adjacent triangle add up to a flat angle (180), so they are adjacent complementary angles. Then draw a straight line parallel to the opposite side of this angle from the vertex of this inner angle and divide that diplomacy into two angles. It can be proved that the other two angles of the triangle are equal to the two angles of this diplomatic division by using two straight lines parallel, at the same angle and at the same angle. Then the sum of the three internal angles of a triangle is equal to which internal angle plus its adjacent complementary angle, which is 180.

6. Mark three triangles with the same size with the letters A, B and C at the positions corresponding to the three angles, and then put the angle A of the first triangle, the angle B of the second triangle and the angle C of the third triangle together. At this time, their lower side (or upper side) just forms a straight line, that is, three angles form a right angle. In other words, the sum of the degrees of the three angles is 65438.

7. Make a parallel line from one vertex to the other and prove it with the inner angle.

It can be concluded that the sum of the internal angles of a triangle is a right angle, that is, 180.