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The image shows a geometric problem with a triangle, where you are asked to find the size of angle \( \angle ABC \).

### Given:
- \( AC = BC \), meaning triangle \( ABC \) is isosceles.
- \( AC \) and \( BC \) are equal, and \( \overrightarrow{ACB} \) is a straight line.

### Steps to solve:

1. Since \( AC = BC \), the two base angles of the isosceles triangle \( \triangle ABC \) (angles \( A \) and \( B \)) are equal. So, \( \angle ABC = \angle BAC \).
   
2. The given angle at \( \angle ACB = 40^\circ \) (marked in the diagram) is external, forming a straight line. Hence:
   \[
   \angle ACB + 2 \times \angle ABC = 180^\circ
   \]
   Using the value of \( \angle ACB \):
   \[
   40^\circ + 2 \times \angle ABC = 180^\circ
   \]

3. Solving for \( \angle ABC \):
   \[
   2 \times \angle ABC = 180^\circ - 40^\circ = 140^\circ
   \]
   \[
   \angle ABC = \frac{140^\circ}{2} = 70^\circ
   \]

Thus, the size of \( \angle ABC \) is **70°**.

Would you like more details on any part of the solution or have further questions?

### Related Questions:
1. How do you find angles in an isosceles triangle?
2. What is the relationship between internal and external angles in a triangle?
3. How do you calculate the sum of angles in any triangle?
4. Can an isosceles triangle have an angle greater than 90°?
5. How does knowing that a triangle is isosceles help in solving angle problems?

### Tip:
Always check for symmetry in isosceles triangles, as equal sides imply equal base angles.

The image shows a geometric problem with a triangle, where you are asked to find the size of angle \( \angle ABC \).

Learn how to find the size of angle \( \angle ABC \) in an isosceles triangle given an exterior angle. This problem covers key geometric concepts, including the Isosceles Triangle Theorem and the Exterior Angle Theorem. Suitable for students in Grades 6-8.

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