Angle ABC is a straight angle (180°) as it's supplementary to angle BAC (90°). Therefore, angle BCD is also 180°.
To calculate the size of angle BCD, we first need to identify the type of triangle ABC. Since we know the measure of two of its angles (90° and 129°), we can determine that triangle ABC is a right triangle.
In a right triangle, the sum of the two acute angles is always 90°. Therefore, we can calculate the measure of angle ABC by subtracting the measure of angle BAC from 90°:
Angle ABC = 90° - Angle BAC = 90° - 90° = 0°
This means that angle ABC is a straight angle. Since angle BCD is supplementary to angle ABC, we can calculate its measure by subtracting the measure of angle ABC from 180°:
Angle BCD = 180° - Angle ABC = 180° - 0° = 180°
Therefore, the size of angle BCD is 180°.