The answer process is as follows:

180 ÷( 1+2+2)

= 180 ÷5

=36

The vertex angle of this triangle is 36 degrees.

Extended data

Nature:

1, and the two base angles are equal;

2. The bisector of the top corner, the median line of the bottom edge and the height coincide with each other;

3. When the waist length is equal to the bottom length, the bottom angle and the top angle are 6.

Theorem:

If two sides of a triangle are equal, then the diagonals of the two sides are also equal. This theorem is listed in Euclid's Elements of Geometry and is called Donkey Bridge Theorem and Isosceles Triangle Theorem.

Donkey Bridge Theorem is a difficult proposition in front of original geometry and a threshold of mathematical ability. People who can't understand this proposition may not be able to handle the more difficult proposition behind it.

The inverse theorem of donkey bridge theorem is: if the two angles of a triangle are equal, the opposite sides of the two angles are equal.

Consistency:

If two isosceles triangles are equal in waist and base, they can be proved to be equal by SSS congruence, and the angle of the triangle can be found by cosine theorem.