In an isosceles triangle ABC (AB = AC), the height BD is drawn to the base. Find the angle ABD if the angle BCA = 40.

If triangle ABC is isosceles, then the angles at the base are equal, i.e. BCA = CAB = 40.

Next, consider a right-angled triangle ABD.

The angle ABD is calculated by the formula: the sum of the angles of the triangle is 180.

angle ABD + angle DAB + angle BDA = 180;

angle ABD = 180 – angle BDA + angle DAB;

angle ABD = 180 – 90 + 40;

angle ABD = 50.

Answer: angle ABD = 50.