Calculator
Example Data Table
| Problem Type | Input | Main Result | Use Case |
|---|---|---|---|
| Regular polygon | 6 sides | Each interior angle = 120° | Hexagon geometry |
| Triangle sides | 3, 4, 5 | Angles = 36.87°, 53.13°, 90° | Right triangle check |
| Ratio angles | Total 180°, ratio 2:3:4 | 40°, 60°, 80° | Shared straight angle |
| Missing angle | Total 180°, known 45°, 65° | Missing angle = 70° | Triangle worksheet |
Formula Used
Regular Polygon
Interior angle sum = (n - 2) × 180°
Each interior angle = [(n - 2) × 180°] ÷ n
Each exterior angle = 360° ÷ n
Central angle = 360° ÷ n
Triangle From Side Lengths
Angle A = cos⁻¹[(b² + c² - a²) ÷ 2bc]
Angle B = cos⁻¹[(a² + c² - b²) ÷ 2ac]
Angle C = 180° - A - B
Angles From Ratio
One ratio unit = Total angle ÷ Sum of ratio parts
Each angle = Its ratio part × One ratio unit
Missing Angle
Missing angle = Total angle - Sum of known angles
How to Use This Calculator
- Select the calculation type from the first field.
- For a regular polygon, enter the number of sides.
- For triangle sides, enter side a, side b, and side c.
- For ratio problems, enter the total angle and ratio parts.
- For missing angles, enter the total and all known angles.
- Press the calculate button to view the result above the form.
- Use the CSV or PDF button to save your result.
Degree Measure of Each Angle Guide
A degree measure tells how wide an angle opens. It helps compare corners in polygons, triangles, paths, diagrams, and classroom drawings. This calculator supports several common angle tasks. It can find each angle in a regular polygon. It can solve triangle angles from three side lengths. It can divide a straight, round, or custom angle by a ratio. It can also find a missing angle from known values. Clear steps make every stored answer easier to audit, compare, and explain later.
Why Angle Measures Matter
Angles connect many parts of mathematics. A polygon needs angle sums to confirm its shape. A triangle needs angle checks to prove it is valid. Ratio based angle problems need fair sharing of one total measure. These ideas appear in geometry, trigonometry, construction sketches, map bearings, and design layouts. Exact degree values reduce mistakes.
Regular Polygon Angles
A regular polygon has equal sides and equal interior angles. Its interior angle sum is found by subtracting two from the number of sides, then multiplying by 180. Dividing that sum by the side count gives each interior angle. The exterior and central angles each equal 360 divided by the number of sides.
Triangle Angle Solving
For triangles, side lengths can reveal angle measures. The calculator uses the law of cosines. It checks the triangle inequality first. Each side must work with the other two sides. When the sides are valid, inverse cosine converts each angle ratio into degrees. The final angle sum should be close to 180 degrees.
Ratio and Missing Angle Problems
Many worksheets give angles in a ratio, such as 2:3:4. The calculator adds the ratio parts. It then multiplies each part by the total angle divided by the ratio sum. Missing angle mode adds known angles and subtracts them from the selected total. This works for triangles, quadrilaterals, full turns, or custom totals.
Good Input Habits
Use positive numbers only. Keep side lengths in the same unit. Enter ratio parts with commas, spaces, or colons. Check that known angles do not exceed the total. Review the step list before saving results. Export the table when you need a record for homework, notes, tutoring, or lesson planning.
FAQs
What does degree measure mean?
Degree measure tells how large an angle is. A full turn has 360 degrees. A straight angle has 180 degrees. A right angle has 90 degrees.
Can this calculator find each angle of a regular polygon?
Yes. Enter the number of sides and choose regular polygon mode. The tool finds the interior sum, each interior angle, each exterior angle, and central angle.
Can I calculate triangle angles from side lengths?
Yes. Choose triangle sides mode. Enter all three side lengths. The calculator checks if the triangle is valid, then uses the law of cosines.
What ratio format can I enter?
You can enter ratio parts with colons, commas, spaces, or semicolons. Examples include 2:3:4, 2 3 4, and 2, 3, 4.
How do I find a missing angle?
Choose missing angle mode. Enter the total angle and the known angles. The calculator subtracts the known angle sum from the selected total.
What total angle should I use for a triangle?
Use 180 degrees for a triangle. A triangle always has an interior angle sum of 180 degrees in standard Euclidean geometry.
What total angle should I use for a full turn?
Use 360 degrees for a full turn. This is useful for circle, central angle, bearing, and complete rotation problems.
Can I download my result?
Yes. After calculating, use the CSV button for spreadsheet data. Use the PDF button for a simple printable report.