In triangle ABC, the height CD divides the angle into two angles, the angle ACD being 25 °, and the angle BCD being 40 °

In triangle ABC, the height CD divides the angle into two angles, the angle ACD being 25 °, and the angle BCD being 40 °. Prove that triangle ABC is isosceles and indicate its sides.

1. We calculate the value of the angle C:
Angle C = angle AСD + ВСD = 25 ° + 40 ° = 65 °.
2. The AСD triangle is rectangular, since the СD is the height. The ADС angle is straight.
3. We calculate the magnitude of the СAD angle, based on the fact that the total value of all angles
triangle is 180:
СAD angle = 180 ° – 25 ° – 90 ° = 65.
4. Angle СAD = angle ACВ = 65 °. Therefore, the AСD triangle is isosceles, since the angles
at the base of the AS are equal, as required.
The sides of this triangle are AB and BC.