What Is an Obtuse Angle?
An obtuse angle measures more than 90° but less than 180°. It opens wider than a square corner, which is a right angle, but not as wide as a straight line.
Obtuse Angle Example
A 95° angle is obtuse because it is just larger than 90°. A 120° angle is obtuse too. An angle of exactly 90° is a right angle, while exactly 180° is a straight angle. Neither one is obtuse.
Obtuse Angle and Acute Angle
An acute angle is smaller than a right angle. An obtuse angle is larger than a right angle but smaller than a straight angle.
| Angle measure | Type |
|---|---|
| 45° | Acute |
| 90° | Right |
| 120° | Obtuse |
| 180° | Straight |
Obtuse Angle Pronunciation
Obtuse angle is pronounced uhb-TOOS ANG-guhl. The stress in “obtuse” is on the second syllable: toose.
Obtuse Angle Properties
An angle is formed by two rays that meet at a point called the vertex. An angle’s measure tells how wide its opening is, or how much one ray turns from the other.
An obtuse angle’s measure is always between 90° and 180°, not including those endpoints. The length of its rays and the direction it points do not change its measure.
Obtuse Angle Opposite: What Happens When Two Lines Cross?
When two straight lines cross, the angles opposite each other are equal. These are called vertical angles. If one of them is obtuse, the opposite angle is obtuse too. For example, an angle of 120° has an opposite angle of 120°.
The angles next to that pair each measure 60°, because angles along a straight line add up to 180°.
Obtuse Angle Triangle
An obtuse triangle has one obtuse angle. For example, a triangle with angles of 110°, 40°, and 30° is obtuse.
A triangle cannot have two obtuse angles. Two angles greater than 90° would already add up to more than 180°, but a triangle’s angles add up to exactly 180°.
Obtuse Angle Shape: Where Can You See One?
An angle is not a closed shape by itself. It is an opening formed where two rays meet. An obtuse angle can be one corner of a larger shape, such as an obtuse triangle.
In a drawing, an angle can point up, down, or sideways and still be obtuse. Look at the opening marked by the curved angle symbol rather than the direction of the drawing.
Obtuse Angle Formula
There is no special formula for an obtuse angle. To check whether an angle is obtuse, compare its measure with 90° and 180°: it must be greater than 90° and less than 180°.
For a triangle with a missing angle, subtract the two known angles from 180°. For example, if the known angles are 30° and 40°, the missing angle is 110°, which is obtuse.
Try It with a Paper Corner
Use the corner of a sheet of paper as a right-angle guide:
- Find the square corner, which represents 90°.
- Draw two rays that meet at one point and make an opening wider than that corner.
- Stop before the rays form a straight line.
The angle you drew is obtuse. You can turn the paper or make the rays longer, and its angle type will stay the same.
Practice: Is 135° Obtuse?
Is a 135° angle obtuse?
Yes. It is greater than 90° and less than 180°, so it is obtuse.