Angle Calculator

Calculate complementary, supplementary, and vertical angles. Convert between degrees, radians, and gradians. Find angles in polygons and solve for missing angles.

📐 Geometry📐 Complementary: A + B = 90°🔢 Math
Calculate
Angle A (degrees)
Number of sides n (polygon mode)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Angle Calculator—Complementary: A + B = 90°degrees/radians

Step-by-Step Examples

Example 1
Complementary

Find angle complementary to 35°.

  • 90°−35°=55°
  • Two angles summing to 90° are complementary
✓ 55°
Example 2
Convert to Radians

Convert 90° to radians.

  • 90 × π/180 = π/2 ≈ 1.5708 rad
✓ π/2 radians
Example 3
Hexagon Angles

Sum of interior angles of a hexagon.

  • n=6: sum=(6−2)×180=720°
  • Each interior angle=720/6=120°
✓ Each angle = 120°

Real-World Applications

📐
Geometry
Angle relationships are fundamental to every geometric proof.
🏗️
Architecture
Roof pitches, structural angles, and design angles all need calculation.
🧭
Navigation
Bearings, headings, and course corrections measured in degrees.
💻
Programming
Trigonometric functions use radians; conversion is essential in code.

Common Mistakes to Avoid

⚠️
Radians vs degrees

Radians are the natural unit (arc length = radius). Always convert to radians before using sin(), cos(), tan() in programming.

⚠️
Exterior angle sum is always 360°

For any convex polygon, exterior angles sum to 360°. Each exterior angle = 360°/n for regular polygons.

⚠️
Vertical angles are equal

When two lines intersect, opposite angles are equal. This is not the same as supplementary angles.

Frequently Asked Questions

What are complementary angles? ▾
Two angles that sum to 90°. Each is the complement of the other.
What are supplementary angles? ▾
Two angles that sum to 180°. Each is the supplement of the other. Linear pairs are supplementary.
What is a radian? ▾
The angle subtended at the center of a circle by an arc equal in length to the radius. 2π radians = 360°, π radians = 180°.
What are vertical angles? ▾
When two lines intersect, the angles across from each other (not adjacent) are vertical angles. They are always equal.
What is a transversal? ▾
A line crossing two parallel lines creates corresponding angles (equal), alternate interior angles (equal), and co-interior angles (supplementary). Used in geometry proofs.

Related Math Calculators

📐 Degrees/Radians📐 Trig Functions📐 Heron Formula📐 Regular Polygon📐 Pythagorean Theorem

Formula Explorer connections

Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.

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