What is an Obtuse Angle?

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Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. Think of it as an angle that is wider than a right angle but not as wide as a straight line.

Simple Example

Quick Example

Imagine the hands of a clock at 4 o'clock. The angle formed between the hour hand and the minute hand is an obtuse angle. It's clearly wider than the right angle formed at 3 o'clock.

Worked Example

Step-by-Step

Let's check if an angle measuring 120 degrees is an obtuse angle.
---Step 1: Recall the definition of an obtuse angle. It must be greater than 90 degrees.
---Step 2: Check if 120 degrees is greater than 90 degrees. Yes, 120 > 90.
---Step 3: Recall the second part of the definition. It must be less than 180 degrees.
---Step 4: Check if 120 degrees is less than 180 degrees. Yes, 120 < 180.
---Conclusion: Since 120 degrees is both greater than 90 degrees and less than 180 degrees, it is an obtuse angle.

Why It Matters

Understanding angles is super important in many fields! Engineers use obtuse angles when designing bridges or buildings to ensure stability. In computer graphics, knowing angle types helps create realistic 3D models and animations, like those in your favorite video games.

Common Mistakes

MISTAKE: Thinking an obtuse angle can be 90 degrees or 180 degrees. | CORRECTION: An obtuse angle must be strictly GREATER than 90 degrees and strictly LESS than 180 degrees. It cannot be equal to 90 or 180.

MISTAKE: Confusing an obtuse angle with an acute angle. | CORRECTION: An acute angle is small (less than 90 degrees), like the angle of a pizza slice. An obtuse angle is wider (more than 90 degrees).

MISTAKE: Not understanding that the 'opening' of the angle matters, not just the length of the lines. | CORRECTION: The size of an angle is measured by how much one arm rotates from the other, not by how long the lines (arms) are drawn.

Practice Questions

Try It Yourself

QUESTION: Is an angle of 150 degrees an obtuse angle? | ANSWER: Yes

QUESTION: An angle measures 95 degrees. Is it an obtuse angle? Why or why not? | ANSWER: Yes, because it is greater than 90 degrees and less than 180 degrees.

QUESTION: If a clock shows the time 5 o'clock, is the smaller angle formed between the hands acute, right, or obtuse? | ANSWER: Obtuse. (At 5 o'clock, the angle is 150 degrees, which is obtuse.)

MCQ

Quick Quiz

Which of the following angle measurements represents an obtuse angle?

45 degrees

90 degrees

110 degrees

180 degrees

The Correct Answer Is:

An obtuse angle is between 90 and 180 degrees. 45 degrees is acute, 90 degrees is a right angle, and 180 degrees is a straight angle. Only 110 degrees fits the definition.

Real World Connection

In the Real World

Next time you see a 'chakri' or a 'fan' in a village fair, notice the angles between its spokes. Or think about the angle your arm makes when you are about to throw a cricket ball – often, it's an obtuse angle before the final swing. Even the angle of the ramp for a wheelchair is carefully designed using angles to ensure it's safe and accessible.

Key Vocabulary

Key Terms

ANGLE: The space between two intersecting lines or surfaces at or close to the point where they meet. | RIGHT ANGLE: An angle that measures exactly 90 degrees. | ACUTE ANGLE: An angle that measures less than 90 degrees. | STRAIGHT ANGLE: An angle that measures exactly 180 degrees.

What's Next

What to Learn Next

Great job understanding obtuse angles! Now that you know about different types of angles, you're ready to explore how angles are used in shapes like triangles and quadrilaterals. This will help you understand geometry even better!