An obtuse angle is any angle greater than 90° but less than 180°. In Honors Geometry, you use it to classify shapes, solve triangle angle problems, and read diagrams correctly.
An obtuse angle in Honors Geometry is an angle with a measure greater than 90 degrees and less than 180 degrees. It opens wider than a right angle, but it is not a straight angle, which measures exactly 180 degrees.
You will usually identify an obtuse angle by measurement, by comparing it to a right angle, or by solving for an unknown angle in a diagram. If the angle is drawn without a number, its size is not always obvious just by looking, so geometry problems often expect you to reason from angle relationships instead of guessing from the picture.
One easy way to picture it is to compare three angle types: acute angles are smaller than 90 degrees, right angles are exactly 90 degrees, and obtuse angles are in between 90 and 180 degrees. That middle range matters a lot in geometry because angle type can change how you classify a figure. For example, a triangle with one obtuse angle is an obtuse triangle, and the other two angles must be acute because all three interior angles still add to 180 degrees.
This is where the Triangle Sum Theorem shows up. Suppose a triangle has angles of 120 degrees and 25 degrees. The last angle must be 35 degrees, which keeps the total at 180 degrees. Since one angle is greater than 90 degrees, the triangle is obtuse. That kind of reasoning is common in Honors Geometry problems, especially when the triangle is labeled with expressions instead of numbers.
Obtuse angles also show up outside triangles, including quadrilaterals and angle pairs formed by intersecting lines. When you are measuring with a protractor, an angle greater than 90 degrees but less than 180 degrees is obtuse, even if the diagram looks close to a right angle. The main habit is to check the measure carefully, because a small estimation mistake can change the entire classification of the figure.
Obtuse angles matter in Honors Geometry because angle type is often the first clue you use to classify a figure and choose the right theorem. If you know an angle is obtuse, you can narrow down whether a triangle is acute, right, or obtuse, and that changes the way you solve the problem.
You also need obtuse angles when working with angle measures written as expressions. A problem might give you one obtuse angle in a triangle and ask for the missing angles using the Triangle Sum Theorem. If you misread the angle as acute, your setup can still look algebraically correct but lead to the wrong classification.
This term also connects to angle relationships in diagrams. In intersecting lines, supplementary angles can create one obtuse angle and one acute angle. In polygon problems, spotting an obtuse interior angle can help you reason about shape, symmetry, and whether a figure is drawn to scale or just sketched for reference.
In class, this shows up in practice problems, constructions, and proof work. You might be asked to mark an obtuse angle, measure it with a protractor, or explain why a triangle cannot have two obtuse angles. That last idea is a common reasoning check, since two angles greater than 90 degrees would already total more than 180 degrees, which cannot happen in a triangle.
Keep studying Honors Geometry Unit 1
Visual cheatsheet
view galleryAcute Angle
An acute angle is smaller than 90 degrees, so it sits on the other side of the right angle benchmark from an obtuse angle. In triangle problems, if one angle is obtuse, the other two must be acute. That contrast is useful when you are classifying triangles or checking whether a diagram is consistent with the angle sum.
Right Angle
A right angle measures exactly 90 degrees, which makes it the dividing line between acute and obtuse angles. In Honors Geometry, you often compare an unknown angle to a right angle first, then decide whether it is smaller, equal, or larger. A lot of classification questions start with that simple comparison.
Triangle Sum Theorem
The Triangle Sum Theorem tells you that the three interior angles of any triangle add to 180 degrees. That is what lets you prove a triangle is obtuse or find a missing angle when one angle is greater than 90 degrees. It is one of the main tools for solving obtuse-angle problems in this course.
Exterior Angle Theorem
The Exterior Angle Theorem connects an exterior angle to the two remote interior angles of a triangle. Since exterior angles are supplementary to interior angles, spotting an obtuse interior angle can help you predict whether the matching exterior angle is acute. These relationships come up a lot in algebraic triangle problems.
A quiz problem may give you a diagram and ask you to name the obtuse angle, measure it, or use it to classify a triangle. The move is usually simple: compare the angle to 90 degrees, then use the triangle angle sum if any angle measures are missing. If the angle is written as an expression, set up the equation carefully so the obtuse angle ends up greater than 90 degrees and less than 180 degrees. You may also need to explain why a triangle cannot have more than one obtuse angle. On written problems, teachers often want both the answer and the reasoning, not just the label.
These are easy to mix up because both are not right angles. An acute angle is less than 90 degrees, while an obtuse angle is greater than 90 degrees but less than 180 degrees. A quick check against the right angle benchmark keeps them straight.
An obtuse angle is greater than 90 degrees and less than 180 degrees.
In a triangle, one obtuse angle means the other two angles must be acute.
The Triangle Sum Theorem is the main tool for finding missing angles around an obtuse angle.
A diagram can look misleading, so measure or calculate the angle instead of guessing from the drawing.
If an angle is exactly 90 degrees, it is right, not obtuse.
It is an angle that measures more than 90 degrees and less than 180 degrees. In Honors Geometry, you use that range to classify angles, triangles, and other figures. The label matters because it can change the way you solve a problem.
Check whether its measure is greater than 90 degrees but still less than 180 degrees. If you do not have a number, use a protractor or solve for the angle with theorems like the Triangle Sum Theorem. Do not rely only on how the sketch looks.
No. Two obtuse angles would already add up to more than 180 degrees, which leaves no room for the third angle. Since every triangle’s interior angles must total 180 degrees, a triangle can have at most one obtuse angle.
No. A right angle is exactly 90 degrees, while an obtuse angle is greater than 90 degrees. That difference is small on paper but huge in geometry problems, because it changes how you classify the angle and the figure.