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.