Isosceles triangle with base AC, angle A is 54 degrees Find the angle ABH if BH is the bisector of the triangle.

Since from the condition of the problem we know that the triangle is isosceles, and the angle at the base a is equal to 54 °, so the second angle at the base c will also be equal to a and equal to 54 °.

Knowing the two angles of the triangle, we can easily find the third, since it is known that the sum of all the angles of a triangle is 180 °.

Thus, we get:

a + b + c = 180 °;

54 ° + b + 54 ° = 180 °;

108 ° + b = 180 °;

b = 180 ° – 108 °;

b = 72 °.

Since we know from the problem statement that BH is a bisector, then the angle ABH = the angle HBC.

So it will be true that:

angle ABH = b / 2;

Thus, the angle ABH = 72 ° / 2 = 36 °.

Answer: 36 °.