In an isosceles triangle ABC, the base AC is an angle C = 30 degrees BD, the median is, determine the angles ABD.

Since triangle ABC is isosceles with base AC, then
∠ А = ∠ С = 30 °.

BD is the median drawn to the base, so it is also the height.

Therefore, ∠ D in triangle ABD is right-angled, that is, equal to 90 °.

Let’s find ∠ В of the triangle ABD, using the knowledge about the sum of the angles of the triangle:

∠ B = 180 ° – ∠ A – ∠ D = 180 ° – 30 ° – 90 ° = 60 °.

Answer: the angles of the triangle ABD have degree measures of 30 °; 60 ° and 90 ° respectively.