Calculator Inputs
Choose a mode, enter values, and press calculate to display the answer above this form.
Example Data Table
| Shape | Sides | Angle Sum | Regular Interior Angle |
|---|---|---|---|
| Triangle | 3 | 180° | 60° |
| Quadrilateral | 4 | 360° | 90° |
| Pentagon | 5 | 540° | 108° |
| Hexagon | 6 | 720° | 120° |
| Octagon | 8 | 1080° | 135° |
Formula Used
General polygon angle sum: Sum of interior angles = (n − 2) × 180°.
Regular polygon interior angle: Each interior angle = ((n − 2) × 180°) ÷ n.
Triangle missing angle: Missing angle = 180° − (first angle + second angle).
Quadrilateral missing angle: Missing angle = 360° − (three known angles).
Polygon missing angle: Missing angle = total polygon sum − sum of known interior angles.
How to Use This Calculator
- Select the calculation mode that matches your geometry problem.
- Enter the required values, such as sides or known angles.
- Click the calculate button to show the result above the form.
- Review the angle values, total sums, and formula summary.
- Use the export buttons to save your result as CSV or PDF.
Frequently Asked Questions
1. What does this interior angle calculator solve?
It solves regular polygon angle values, missing polygon angles, missing triangle angles, and missing quadrilateral angles using standard geometry rules.
2. What is an interior angle?
An interior angle is the angle formed inside a polygon where two adjacent sides meet. Every polygon has one interior angle at each vertex.
3. How do you find the sum of polygon interior angles?
Use the formula (n − 2) × 180°, where n is the number of sides. This gives the full interior-angle sum for any simple polygon.
4. How do regular polygon angles differ?
In a regular polygon, all sides and all interior angles are equal. Divide the total interior-angle sum by the number of sides to get one angle.
5. Can this calculator help with school geometry?
Yes. It is useful for homework, revision, classroom demonstrations, and checking manual geometry calculations quickly and clearly.
6. Why must a triangle total 180 degrees?
A triangle always has an interior-angle sum of 180 degrees in Euclidean geometry. That fixed rule lets you find a missing third angle immediately.
7. Why must a quadrilateral total 360 degrees?
A quadrilateral can be split into two triangles. Since each triangle totals 180 degrees, the full quadrilateral totals 360 degrees.
8. What do the CSV and PDF buttons export?
They export the displayed result details, including the chosen mode, calculated values, and formula summary, so you can save or share your work.