Understanding Triangle Angles
In Euclidean geometry, the interior angles of any triangle always sum to exactly 180 degrees (or pi radians). This fundamental property allows us to classify triangles by their angles and to find a missing angle when two are known.
Triangle Classifications by Angle
Acute Triangle
All three interior angles are less than 90 degrees.
A < 90, B < 90, C < 90
Right Triangle
Exactly one interior angle is exactly 90 degrees.
One angle = 90
Obtuse Triangle
Exactly one interior angle is greater than 90 degrees.
One angle > 90
Equilateral Triangle
All three interior angles are exactly 60 degrees.
A = B = C = 60
Degrees vs. Radians
Degrees and radians are two units for measuring angles. A full circle is 360 degrees or 2pi radians. To convert between them:
- Degrees to Radians: radians = degrees x (pi / 180)
- Radians to Degrees: degrees = radians x (180 / pi)
- 180 degrees = pi radians (the angle sum of a triangle)
Tips
- If the sum of angles does not equal 180 degrees, the triangle is invalid in Euclidean geometry.
- Each angle must be greater than 0 and less than 180 degrees.
- An isosceles triangle has at least two equal angles; an equilateral has all three equal.