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Let's break down and address each part of the problem based on the uploaded image:

### Part (a) — Is it possible for all the interior angles of an irregular 4-sided shape to be equal?

Yes, it is possible for all the interior angles of a 4-sided shape to be equal even if the sides are not equal. This is because a **rectangle** satisfies this condition. 

- A rectangle has all four angles equal to 90 degrees, but not necessarily equal sides, which means that the shape is irregular (in the sense that the sides may vary in length), yet the angles are still equal.
- A square is a special case where the sides are also equal, but a **non-square rectangle** (with unequal adjacent sides) proves that the interior angles can all be the same in an irregular quadrilateral.

### Part (b) — Is it possible for all the interior angles of an irregular 5-sided shape to be equal?

No, it is not possible for all the interior angles of a 5-sided shape (pentagon) to be equal if the sides are unequal. 

- For a polygon with 5 sides (pentagon), the sum of the interior angles is always \( 540^\circ \). 
- In a regular pentagon, each interior angle measures \( 108^\circ \), and the sides must also be equal to maintain the equality of angles.
- If the sides are not equal (irregular), it would force some angles to change as well, making it impossible for all the interior angles to remain equal while having unequal sides.

Would you like a diagram or further clarification on these points?

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Here are five related questions to expand your understanding:

1. How do you calculate the sum of the interior angles of any polygon?
2. What is the difference between a regular and irregular polygon?
3. Can you name other types of quadrilaterals where the angles might be equal?
4. Why can't an irregular pentagon have equal angles while having unequal sides?
5. What is the formula for finding the measure of each angle in a regular polygon?

**Tip:** For any polygon, the sum of the interior angles can be calculated using the formula \( 180(n - 2) \), where \( n \) is the number of sides.

By writing a sentence or drawing a diagram, show that it is possible for all of the interior angles of an irregular 4-sided shape to be equal. Is it possible for all of the interior angles of an irregular 5-sided shape to be equal? Justify your answer by writing an explanation or drawing a diagram.

Discover whether it is possible for all interior angles of an irregular 4-sided shape to be equal, and why this can't happen in a 5-sided shape. This geometry problem breaks down the angle sum properties of quadrilaterals and pentagons. Suitable for Grades 7-9.

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