https://file.aiquickdraw.com/mathbot/file/1728924867335irf390gs.jpg

In the given image, we need to calculate the size of angle \( \angle BCD \).

### Observations:
- Triangle \( ABC \) is a right triangle with \( \angle A = 90^\circ \).
- \( \angle ABC = 128^\circ \) (indicated in purple).
- We are asked to find \( \angle BCD \), the green angle at point \( C \), where \( D \) is used with the protractor.

### Step-by-Step Solution:

1. **Find \( \angle ACB \):**
   In a triangle, the sum of interior angles is always \( 180^\circ \). So, for triangle \( ABC \):
   \[
   \angle A + \angle ABC + \angle ACB = 180^\circ
   \]
   Since \( \angle A = 90^\circ \) and \( \angle ABC = 128^\circ \), we can solve for \( \angle ACB \):
   \[
   90^\circ + 128^\circ + \angle ACB = 180^\circ
   \]
   \[
   \angle ACB = 180^\circ - 218^\circ = -38^\circ
   \]
   This indicates that there's an issue. Let's recheck. For this problem to make sense geometrically (and for acute angle relationships), triangle settings need to follow constraints that seem inconsistent in this case

Learn how to calculate the size of angle BCD in a right-angle triangle. This problem involves using the Triangle Angle Sum Theorem and understanding interior angle relationships, with step-by-step instructions for precise protractor measurement. Suitable for students in Grades 6-8.

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