Rectangle Angles Analysis: Can a Rectangle Have an Acute Angle?

Rectangle Properties with Angle Classification

True or false?

One of the angles in a rectangle may be an acute angle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Can there be an acute angle in a rectangle?
00:03 Let's draw a rectangle
00:09 By definition, all angles in a rectangle are right angles
00:14 Therefore, there cannot be an acute angle in a rectangle
00:20 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

True or false?

One of the angles in a rectangle may be an acute angle.

2

Step-by-step solution

One of the properties of a rectangle is that all its angles are right angles.

Therefore, it is not possible for an angle to be acute, that is, less than 90 degrees.

3

Final Answer

False

Key Points to Remember

Essential concepts to master this topic
  • Definition: All four angles in a rectangle are exactly 90 degrees
  • Classification: 90° = right angle, < 90° = acute, > 90° = obtuse
  • Verification: Sum all angles: 90° + 90° + 90° + 90° = 360° ✓

Common Mistakes

Avoid these frequent errors
  • Confusing rectangles with other quadrilaterals
    Don't think rectangles can have acute angles like triangles = wrong shape identification! This confuses rectangles with parallelograms or other quadrilaterals that can have varying angles. Always remember rectangles are special quadrilaterals where every angle must be exactly 90°.

Practice Quiz

Test your knowledge with interactive questions

Look at the angles shown in the figure below.

What is their relationship?

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FAQ

Everything you need to know about this question

What makes a rectangle different from other quadrilaterals?

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A rectangle has four right angles (90°) and opposite sides that are parallel and equal. This is what makes it special - no other quadrilateral has all four angles exactly 90°!

Can any angle in a rectangle be less than 90°?

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No, never! If even one angle is less than 90° (acute), then the shape is not a rectangle. It might be a parallelogram or another quadrilateral, but not a rectangle.

What's the difference between acute, right, and obtuse angles?

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  • Acute: Less than 90°
  • Right: Exactly 90°
  • Obtuse: Greater than 90° but less than 180°

Rectangles only have right angles!

Why do all angles in a rectangle add up to 360°?

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This is true for all quadrilaterals! Since rectangles have four 90° angles: 90° + 90° + 90° + 90° = 360°. This confirms our rectangle is correct.

If I see a shape with one acute angle, can it still be a rectangle?

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Absolutely not! The moment you have an acute angle (less than 90°), the shape cannot be a rectangle by definition. It's a different type of quadrilateral.

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