
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
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