Interior angles of a triangle
The interior angles are those on the inside of the triangle.
Try this Drag the orange dots on each vertex A,B or C to reshape the triangle. Notice that the interior angles always add to 180°

The interior angles of a triangle always add up to 180°. Because of this, only one of the angles can be 90° or more. In a right triangle, since one angle is always 90°, the other two must always add up to 90°

A triangle is simply a polygon that has 3 sides. See interior angles of a polygon for the properties of the interior angles of a polygon with any number of sides.

Properties

  • The interior angles of a triangle always add up to 180°
  • Because the interior angles always add to 180°, every angle must be less than 180°
  • The bisectors of the three interior angles meet at a point, called the incenter, which is the center of the incircle of the triangle.

Note

The interior angles only add to 180° when the triangle is planar, meaning it is lying on a flat plane. If the triangle is not planar, for example if it is lying on the curved surface of a sphere, the angles do not add to 180°.

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises