Quadrilateral Angles Calculator
Calculate missing angles in quadrilaterals. The sum of all interior angles equals 360°.
Angles
Enter at least 3 angles to calculate the 4th
Calculated Angles:
Angle 1: —°
Angle 2: —°
Angle 3: —°
Angle 4: —°
Step-by-Step Solution:
About Quadrilateral Angles
Angle Sum Property
The sum of all interior angles in any quadrilateral is always 360°. This is true for all quadrilaterals: squares, rectangles, parallelograms, trapezoids, rhombuses, kites, and irregular quadrilaterals.
Special Cases
Rectangle/Square: All angles = 90°
Parallelogram: Opposite angles equal, consecutive angles sum to 180°
Trapezoid: Angles on same leg are supplementary (in isosceles trapezoid)
Kite: One pair of opposite angles are equal
Why 360°?
A quadrilateral can be divided into two triangles by drawing one diagonal. Since each triangle has angles summing to 180°, the quadrilateral's angles sum to 2 × 180° = 360°.
Applications
- Finding missing angles in geometry problems
- Verifying if measurements form a valid quadrilateral
- Architecture and engineering design
- Computer graphics and game development
Frequently Asked Questions
Do all quadrilaterals have 360° angle sum?
Yes, every quadrilateral, regardless of its shape or type, has interior angles that sum to exactly 360°.
How many angles do I need to find the rest?
For a general quadrilateral, you need at least 3 angles to find the 4th. For special quadrilaterals like parallelograms, knowing one angle is enough due to their special properties.
Can a quadrilateral have all different angles?
Yes, an irregular quadrilateral can have four different angles, as long as they sum to 360°.
What if my angles don't add up to 360°?
If the angles don't sum to 360°, there's an error in measurement or the shape is not a valid planar quadrilateral. Double-check your measurements.
What's the largest possible angle in a quadrilateral?
In a convex quadrilateral, each angle must be less than 180°. In a concave quadrilateral, one angle can be greater than 180° (reflex angle), but the sum must still be 360°.
How do I verify my quadrilateral is valid?
Check that all four angles sum to 360°. Also verify that the shape can physically exist (triangle inequality for sides, angles within valid ranges).