X Tables
geometry

Acute obtuse and reflex angles

Compare angles as smaller or larger than a right angle.

Quick answer

Angles are measured in degrees and can be classified as acute (less than 90°), obtuse (between 90° and 180°), or reflex (more than 180° but less than 360°).

Learning outcome

By the end of this page, you will be able to identify and name acute, obtuse, and reflex angles in everyday objects and shapes. Success signs:
  • You can tell the difference between angles that are smaller than a right angle, larger than a right angle, and larger than a straight line
  • You can name angles as acute, obtuse, or reflex
  • You can find examples of these angles in your home, school, or playground
  • You can draw or show these angles using your hands or a protractor

Why this matters

Understanding angles helps you see the world around you more clearly. You use angles when you turn a door, when you look at a clock, when you play football, or when you build with blocks. Knowing the difference between acute, obtuse, and reflex angles helps you understand how shapes fit together and how objects move. This knowledge will help you in your maths lessons and in real life, like when you're measuring things or planning where to put furniture.

How it works

Angles are formed when two lines meet at a point. We measure angles in degrees (°). A right angle is exactly 90°. We can compare any angle to a right angle to see what kind it is:
  • Acute angles are smaller than a right angle (less than 90°)
  • Obtuse angles are between a right angle and a straight line (between 90° and 180°)
  • Reflex angles are larger than a straight line but less than a full turn (more than 180° but less than 360°)
To understand this better, imagine you're a robot with a rotating arm. When your arm points straight up, that's 90°. When it points to the right, that's 90° too. When it points to the left, that's 180°. When it points back to the front, that's 360°. Any angle between these points is either acute, obtuse, or reflex.

Examples you can see

Let's look at some examples in everyday life:
  • Acute angles can be seen in the point of a triangle, the corner of a book, or the tip of a slice of pizza
  • Obtuse angles can be seen in the angle between the hands of a clock at 10 o'clock, the corner of a door when it's opened wide, or the angle of a kite flying in the sky
  • Reflex angles can be seen in the angle between the hands of a clock at 4 o'clock, the corner of a room when you look at it from the back, or the angle you make when you turn around in a circle
Let's try a simple example with a protractor. Imagine you have a protractor and you're measuring angles:
  1. Place the protractor on a corner of a shape
  2. Align one side of the shape with the baseline of the protractor
  3. Look at where the other side points on the protractor scale
  4. If it's less than 90°, it's acute
  5. If it's between 90° and 180°, it's obtuse
  6. If it's more than 180° but less than 360°, it's reflex

Try it as a mini adventure

Angle Explorer Quest You are a young explorer in a magical land where angles come alive! Your mission is to find and classify angles in different places. 1st stop: The Garden of Shapes Look around your garden or a park. Find a triangle. What kind of angle is at the point of the triangle? Is it acute, obtuse, or reflex? 2nd stop: The Clock Tower Look at a clock. At 10 o'clock, what angle do the hands make? Is it acute, obtuse, or reflex? 3rd stop: The Playground Find a door. When it's opened wide, what angle does it make? Is it acute, obtuse, or reflex? 4th stop: The Kitchen Look at a pizza. If you cut it into 8 pieces, what angle does each slice make? Is it acute, obtuse, or reflex? 5th stop: The Room Turn around in your room. When you turn halfway, what angle have you made? Is it acute, obtuse, or reflex? 6th stop: The Sky Look at the sun and the horizon. What angle does the sun make with the ground? Is it acute, obtuse, or reflex?

Common mistakes

  • Mistake: Thinking that any angle over 90° is obtuse Why it happens: Confusing the definition of obtuse angles with reflex angles Fix: Remember that obtuse angles are between 90° and 180°, while reflex angles are more than 180° but less than 360°
  • Mistake: Not knowing the difference between acute and right angles Why it happens: Confusing the size of acute angles with right angles Fix: Use a right angle (like the corner of a book) as a reference. Acute angles are smaller than a right angle
  • Mistake: Counting angles incorrectly when they are larger than 180° Why it happens: Not understanding that reflex angles are measured from the inside of the angle Fix: Remember that reflex angles are the bigger part of the angle, not the smaller part

Parent and carer guide

This is a great opportunity to explore angles with your child in a fun, hands-on way. Here's how to help:
  • Use a protractor to measure different angles around your home
  • Draw angles with your child and label them as acute, obtuse, or reflex
  • Play the angle explorer game together
  • Point out examples of angles in daily life, such as the corner of a table or the hands of a clock
  • Use your hands to show different angles: make a right angle with your arms, then a wider angle to show an obtuse angle
  • Don't worry if your child gets confused at first. Angle recognition takes time and practice
  • Encourage your child to explain their thinking when classifying angles

Practice questions

  1. What type of angle is 45°? Answer: Acute
  2. What type of angle is 120°? Answer: Obtuse
  3. What type of angle is 270°? Answer: Reflex
  4. What type of angle is 90°? Answer: Right angle (not acute, obtuse, or reflex)
  5. What type of angle is 180°? Answer: Straight line (not acute, obtuse, or reflex)
  6. What type of angle is 30°? Answer: Acute
  7. What type of angle is 200°? Answer: Reflex
  8. What type of angle is 150°? Answer: Obtuse
  9. What type of angle is 350°? Answer: Reflex
  10. What type of angle is 60°? Answer: Acute

FAQ

What is the difference between acute and obtuse angles?

Acute angles are smaller than a right angle (less than 90°), while obtuse angles are between a right angle and a straight line (between 90° and 180°).

How do I remember which angles are reflex?

Reflex angles are the big angles that are more than 180° but less than 360°. Think of them as the "outside" angles when you turn around in a circle.

Can I measure reflex angles with a regular protractor?

Yes, but you need to measure the smaller angle and subtract it from 360°. For example, if the smaller angle is 90°, the reflex angle is 360° - 90° = 270°.

Why are angles important in real life?

Angles help us understand how shapes fit together, how objects move, and how to measure and build things. They're used in architecture, engineering, art, and even in sports!

What are some examples of acute angles in nature?

Examples include the point of a leaf, the corner of a flower petal, the angle of a bird's wing, or the tip of a mountain.