The angle at the apex of an isosceles triangle is 80 degrees. find an angle between the height

The angle at the apex of an isosceles triangle is 80 degrees. find an angle between the height lowered to the deep side and the base.

By condition, the triangle ABC is isosceles, then its angles at the base of the AC are equal to each other.

Angle BAC = BCA = (180 – ABC) / 2 = (180 – 80) / 2 = 100/2 = 50.

Triangle AHC is rectangular, since AH is the height of triangle ABC.

Then in a right-angled triangle AHC the angle CАH = (180 – AHC – CAH) = (180 – 90 – 50) = 40.

Answer: The angle between height and base is 40.