In triangle BCD, sides BD and CD are equal, DM is the median, angle BDC is 38 °. Find the corners BMD and BDM.

Since BD = CD, the triangle BCD is isosceles (BC is the base).

We use the property of the median in an isosceles triangle: in an isosceles triangle, the median dropped to the base is the height and the bisector.

Therefore, DM is the bisector and the height.

Find the BMD angle.

Since DM is the height, the angle BMD = 90 °.

Find the corner BDM.

Since DM is a bisector, the angles BDM and CDM are equal.

BDC = BDM + CDM = 2 * BDM.

BDM = BDC / 2.

BDM = 38 ° / 2 = 19 °.

Answer: 90 °, 19 °.