Calculate the Interior Angle Sum of a Square: ABCD Geometry Problem

Interior Angle Sum with Square Properties

Look at the square below:AAABBBCCCDDD

What is the sum of the angles in the square?

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Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the square below:AAABBBCCCDDD

What is the sum of the angles in the square?

2

Step-by-step solution

According to the properties of the square, all angles are right angles.

Since there are 4 angles that are all equal to 90 degrees:

4×90=360 4\times90=360

3

Final Answer

360º 360 º

Key Points to Remember

Essential concepts to master this topic
  • Rule: All interior angles of a square are 90 degrees
  • Technique: Multiply number of sides by individual angle: 4 × 90° = 360°
  • Check: Sum equals (n-2) × 180°: (4-2) × 180° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Adding only three angles instead of all four
    Don't count just three angles and get 270° = incomplete sum! This misses one corner and gives the wrong total. Always count all four interior angles of the square: A + B + C + D.

Practice Quiz

Test your knowledge with interactive questions

Look at the square below:

Is a parallelogram a square?

FAQ

Everything you need to know about this question

Why are all angles in a square exactly 90 degrees?

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A square is a special rectangle where all sides are equal length. Since rectangles have four right angles (90°), and squares are rectangles, every corner of a square must be 90°.

Is there a formula for finding angle sums in any polygon?

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Yes! For any polygon with n sides, the interior angle sum is (n-2) × 180°. For a square: (4-2) × 180° = 2 × 180° = 360°.

What if the square looks tilted or rotated in the diagram?

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The orientation doesn't matter! Whether the square sits flat or is rotated, all interior angles are still 90°. The angle sum is always 360° regardless of position.

How is this different from finding the sum for other quadrilaterals?

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All quadrilaterals have the same angle sum of 360°! The difference is that squares have four equal angles (90° each), while other quadrilaterals can have different angle measures.

Can I use this method for other regular polygons?

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Absolutely! For any regular polygon, multiply the number of sides by the measure of each interior angle. For irregular polygons, you'll need to add up each individual angle.

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