Obtuse angles are wide, open angles that measure greater than 90° but less than 180°.
Obtuse angles can measure from 91° to 179°.
Example:
ray ON and ray OP meet at a vertex and form an angle greater than a right angle (greater than 90°).
∠NOP is obtuse.
Look at the angles below. Which is an obtuse angle?
∠BAT is obtuse
Finding Obtuse Angles in the Real World
Obtuse angles can be found all around us! Unlike acute angles, which are small and narrow, obtuse angles are wide and open, appearing in many common objects. Here are some fun examples:
Here are some fun examples:
- A stop sign – The angles formed between the sides of an octagon are obtuse.
- The top part of a clothes hanger – The angle where the two sides of the hanger meet is usually wider than 90°, making it an obtuse angle.
- A clock showing 4:00 – The angle between the hour and minute hands at 4:00.
Since obtuse angles measure between 90° and 180°, they are larger than a right angle but smaller than a straight angle.
Can you find any obtuse angles around your home or classroom?
Measuring an Obtuse Angle with a Protractor
Angles are all around us and can be measured using degrees.
Here are three different examples of obtuse angles—each one is greater than 90° but less than 180°.
You can measure angles using a tool called a protractor.
To measure ∠FAN, follow these steps:
- Line up ray AN with the straight bottom edge (0° line) of the protractor.
- Find where ray AF points on the protractor’s scale.
- Notice that AF passes through 160°, confirming that ∠FAN is an obtuse angle.
Tip: When measuring angles, always check if it is greater than 90° but less than 180° to determine if it’s obtuse!
Practice Problems
Which is an obtuse angle?
Which of the following is an obtuse angle?
An obtuse angle must always be:
An angle measuring 175° is an obtuse angle.
It is greater than 90° but less than 180°.
