Calculating angle...
Choose an angle relationship to solve
The result will show the missing angle, formula, steps, and a labeled geometry diagram.
Geometry angle rules
Angle calculator for missing geometry angles
This angle calculator finds missing angle values from the relationships students use most often in geometry: complementary angles, supplementary angles, vertical angles, and triangle interior angles. Enter the known angle values in degrees and the calculator returns the missing angle, the formula, a substituted equation, and a labeled diagram.
Use it as a complementary angle calculator for right-angle problems, a supplementary angle calculator for straight-line problems, a vertical angles calculator for intersecting lines, or a missing triangle angle calculator when two interior angles are known.
Complementary angles
A + B = 90°
A right angle split into two smaller angles. If A is known, B = 90° - A.
Supplementary angles
A + B = 180°
A straight angle split into two adjacent angles. If A is known, B = 180° - A.
Vertical angles
opposite angles are equal
When two lines cross, opposite angles match and adjacent angles add to 180°.
Triangle angles
A + B + C = 180°
Every triangle has interior angles that add to 180°. The missing angle is 180° - A - B.
Visual angle relationships
The diagrams below show the same angle rules used by the calculator. Teal arcs represent known angles and blue arcs represent calculated or related angles.
How to find a missing angle
1. Identify the relationship. Look for a right angle, a straight line, two crossing lines, or a triangle.
2. Choose the matching mode. Select complementary, supplementary, vertical, or triangle in the calculator.
3. Enter only the known angles. For triangle mode, enter two interior angles. For the other modes, enter one known angle.
4. Check the diagram. The result diagram labels the known and missing angles so you can verify the geometry visually.
When to use each angle rule
- Complementary: use when the two angles form a right angle, such as 32° and 58°.
- Supplementary: use when the two angles form a straight line, such as 125° and 55°.
- Vertical: use when two lines intersect and you need the opposite or adjacent angle values.
- Triangle: use when two interior angles of a triangle are known and the third is missing.
Worked angle examples
| Problem | Formula | Answer |
|---|---|---|
| Complement of 47° | 90° - 47° | 43° |
| Supplement of 120° | 180° - 120° | 60° |
| Vertical angle at 65° | 180° - 65° | Opposite 65°, adjacent 115° |
| Triangle 60° + 75° | 180° - 60° - 75° | 45° |
Common angle mistakes
- Using 180° for a right angle: complementary angles add to 90°, not 180°.
- Mixing adjacent and vertical angles: vertical angles are opposite and equal; adjacent angles usually form a straight line and add to 180°.
- Entering exterior triangle angles: triangle mode expects interior angles only.
- Allowing zero or 180° triangle angles: a valid triangle needs all three interior angles greater than 0°.
Angle calculator FAQ
What is a complementary angle?
Two complementary angles add to 90°. If one angle is 34°, its complement is 56° because 90° - 34° = 56°.
What is a supplementary angle?
Two supplementary angles add to 180°. If one angle is 138°, its supplement is 42° because 180° - 138° = 42°.
Are vertical angles always equal?
Yes. When two straight lines intersect, each pair of opposite angles is equal. Adjacent angles at the same intersection add to 180°.
How do you find a missing triangle angle?
Add the two known interior angles, then subtract that sum from 180°. For example, 180° - 68° - 44° = 68°.
Can an angle calculator use radians?
This calculator is designed for degrees because most school geometry problems use degrees. Convert radians to degrees first if your input is in radians.
Why does the calculator reject 0° or 180° triangle angles?
A triangle with a 0° or 180° interior angle collapses into a line, so it is not a valid triangle.
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Geometry references
These outside resources are useful for reviewing angle definitions, triangle rules, and geometry foundations.