Answer:
(A) 45 degrees
Step-by-step explanation:
Given that triangle BCD is an Isosceles Triangle where BD=CD.
• Then the base angles of Isosceles triangle BCD: ,Angles B and C are congruent and are both 50 degrees.
The sum of the angles in a triangle is 180 degrees, therefore, in triangle BCD:

As can be seen in the diagram below:
Angle D (in triangle BDC) is an exterior angle of opposite interior angles A and B (in triangle BAD).
The sum of opposite interior angles is equal to the exterior angle.

The measure of angle A is 45 degrees.