# Obtuse Angle: Definition, Degrees & Examples

TL;DR  
An obtuse angle is any angle that measures more than 90° and less than 180° — wider than a right angle but not yet a straight line. This article defines the obtuse angle, lists its properties, shows where it appears in real life and in triangles, and clears up the mistakes that trip students up.

## What Is an Obtuse Angle?  
An **obtuse angle** is an angle whose measure is **greater than 90° but less than 180°**. In symbols, an angle ∠ABC is obtuse when 90° < ∠ABC < 180°. It is wider than a right angle (the square 90° corner) and narrower than a straight angle (the flat 180° line).

The word comes from the Latin _obtusus_, meaning "blunt" or "dull" — the opposite of the sharp, narrow **acute angle**. An obtuse angle looks open and blunt: think of the angle at the wide base of an isosceles triangle that has been squashed flat, not the needle-sharp point at its tip.

Because the boundaries are _strict_, 90° itself is not obtuse (that is a right angle) and 180° is not obtuse (that is a straight angle). An obtuse angle lives in the open interval — anything from 91° up to 179° in whole degrees, and every value between.

## Properties of an Obtuse Angle  
The defining range gives the obtuse angle a small set of properties worth holding on to.  
- **Range.** It always satisfies 90° < θ < 180°. Outside that range, the angle is not obtuse.  
- **One per triangle, at most.** A triangle's three angles sum to 180°, so it can hold **at most one** obtuse angle. Two obtuse angles would already exceed 180° on their own.  
- **Its supplement is acute.** Two angles that add to 180° are **supplementary**. The supplement of an obtuse angle is always acute.  
- **Its reflex partner is between 180° and 360°.** For an obtuse angle of θ, that partner is 360° − θ, which lands between 180° and 270°.  
- **It cannot be a right angle's complement.** **Complementary angles** add to 90°, so no obtuse angle has a complement.

## How Do You Identify an Obtuse Angle?  
The fastest check is to compare the angle against a right angle by eye, then confirm with measurement.  
- **By sight:** picture a square corner (90°) at the vertex. If the angle's arms open _wider_ than that corner but have not flattened into a straight line, it is obtuse.  
- **By measure:** read the angle with a protractor. If the reading is between 91° and 179°, it is obtuse. The key habit is deciding _first_ whether the angle looks bigger or smaller than a right angle, then choosing the protractor scale that matches.

## Obtuse Angles Inside a Triangle  
A triangle with one obtuse angle is called an **obtuse triangle**. Its other two angles must both be acute, because the three together can only reach 180°. The side opposite the obtuse angle is always the longest side of the triangle — the wider the angle opens, the longer the side it faces.

## Examples of Obtuse Angles  
### Example 1  
**Is an angle measuring 115° obtuse?**  
Check the range. Since 90° < 115° < 180°, the angle is **obtuse**.

### Example 2  
**An angle measures 90°. A student says it is the smallest obtuse angle. Is that right?**  
_Wrong attempt._ A 90° angle is exactly a right angle. The obtuse band starts _after_ 90°.  
_Correct._ 90° is a right angle, not obtuse. There is no single "smallest obtuse angle".

### Example 3  
**Two angles are supplementary. One of them is 130°. Classify both.**  
The 130° angle is **obtuse**; the other is 50° which is **acute**.

### Example 4  
**An obtuse angle measures 145°. Find the measure of its reflex partner.**  
The reflex partner is 360° − 145° = 215°.

### Example 5  
**In a triangle, two angles measure 35° and 40°. Find the third angle and classify the triangle.**  
The third angle measures 105°, so the triangle is an **obtuse triangle**.

### Example 6  
**The angle ∠XYZ is given by the expression (4k+30)° with k=25. Confirm it is obtuse.**  
Substituting gives: (100+30)° = 130°.  
Since 90° < 130° < 180°, the angle ∠XYZ is indeed **obtuse**.

## Why the Obtuse Angle Matters Beyond the Classroom  
Naming an angle obtuse is important in various fields including physics, engineering, design, navigation, and sports.

## Where Students Trip Up on Obtuse Angles  
### Mistake 1: Treating 90° or 180° as obtuse  
The correct way: Only angles strictly between them are obtuse.

### Mistake 2: Calling a reflex angle obtuse  
The correct way: Check if the angle has crossed 180°.

### Mistake 3: Reading the wrong protractor scale  
The correct way: Judge by eye first and then choose the correct scale.

## Key Takeaways  
- An **obtuse angle** measures strictly more than 90° and strictly less than 180°.  
- The angles named boundaries are not obtuse.  
- A triangle can have at most one obtuse angle, and its longest side is opposite that obtuse angle.

## Practice These Problems to Solidify Your Understanding  
1. Classify each angle as acute, right, obtuse, straight, or reflex: 48°, 90°, 134°, 180°, 300°.  
2. Find the other angle supplementary to 158° and classify both.  
3. Find the third angle in a triangle with angles 25° and 43°, and state whether it is obtuse.