how many degrees are in a quadrilateral
A quadrilateral has 360 degrees in total for its interior angles.
Quick Scoop: Why 360°?
- A quadrilateral is any 4‑sided polygon.
- The sum of its interior angles is always 360°, no matter the shape (square, rectangle, kite, etc.).
- You can use the polygon angle-sum formula:
Sum of interior angles=(n−2)×180∘\text{Sum of interior angles}=(n-2)\times 180^\circ Sum of interior angles=(n−2)×180∘, where nnn is the number of sides.
For a quadrilateral, n=4n=4n=4, so (4−2)×180∘=2×180∘=360∘(4-2)\times 180^\circ =2\times 180^\circ =360^\circ (4−2)×180∘=2×180∘=360∘.
Handy tip for problems
If you know three angles in a quadrilateral, you can find the fourth by:
- Fourth angle =360∘−(sum of the other three angles)=360^\circ -(\text{sum of the other three angles})=360∘−(sum of the other three angles).
So whenever you see a 4‑sided shape in geometry, you can be confident its interior angles always add up to 360°.