In figure abcdef is regular hexagon abqp and bcsr are square <Abc=

To solve for \(\angle ABC\), let's break down the problem:

We are given:
- A regular hexagon \(ABCDEF\).
- Square \(ABQP\), where \(AB\) is one side of the square.
- Square \(BCSR\), where \(BC\) is one side of the square.

### Step 1: Understanding the regular hexagon
In a regular hexagon, all internal angles are 120° and all sides are of equal length. Therefore, the angle at vertex \(B\) in \(\triangle ABC\) (as part of the hexagon) is \(\angle ABC = 120^\circ\).

### Step 2: Analyzing the squares
Both squares \(ABQP\) and \(BCSR\) have right angles, which means:
- \(\angle ABQ = 90^\circ\)
- \(\angle BCS = 90^\circ\)

However, these don't directly affect \(\angle ABC\), since this angle comes from the hexagon structure.

### Conclusion:
Since \(\angle ABC\) is part of a regular hexagon, we can directly conclude:
\[
\boxed{\angle ABC = 120^\circ}
\]

Would you like more details or clarifications on any part of the solution?

### Follow-up questions:
1. How can we calculate angles in other polygons, like octagons?
2. What properties define a regular polygon?
3. Can we explore the relationship between the angles of a hexagon and the squares?
4. How would the result change if the hexagon was not regular?
5. What is the general formula for the interior angles of a polygon?

### Tip:
For any regular polygon, the interior angle can be calculated as \(\frac{(n-2) \times 180^\circ}{n}\), where \(n\) is the number of sides.

Learn how to solve for angle ABC in a regular hexagon (ABCDEF) with squares ABQP and BCSR. This problem explores key geometry concepts such as regular polygons, the properties of hexagons, and angle calculations. Suitable for students in Grades 8-10.

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