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To calculate the size of angle \( \angle BCD \), let's follow these steps:

1. We are given that \( \angle ABC = 128^\circ \).
2. The triangle \( ABC \) seems to form a straight line with the point \( D \) on the line as shown by the protractor.
3. In a straight line, the total angle is \( 180^\circ \). So, using the straight line rule:

\[
\angle BCD + \angle ABC = 180^\circ
\]

4. Substituting the known value for \( \angle ABC \):

\[
\angle BCD + 128^\circ = 180^\circ
\]

5. Solving for \( \angle BCD \):

\[
\angle BCD = 180^\circ - 128^\circ = 52^\circ
\]

Thus, the size of \( \angle BCD \) is \( 52^\circ \).

Would you like further details or have any questions?

Here are some related questions:
1. How can we use the triangle sum theorem in this context?
2. Why is the straight line rule applied to this particular problem?
3. How do supplementary angles help in calculating unknown angles?
4. What other methods can be used to verify the size of an angle?
5. How do angles around a point sum up to a particular value?

**Tip:** When working with straight lines, always remember that the sum of angles along the line is \( 180^\circ \).

Learn how to calculate the size of angle BCD when given the angle ABC. This problem involves the concept of supplementary angles and the Straight Angle Theorem. Suitable for students in Grades 6-8.

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