△ Triangles: Angles and Sides

Triangle Angle Sum = 180°

The three interior angles of any triangle always add up to 180°. This is one of the most fundamental facts in Euclidean geometry. If A = 60° and B = 70°, then C = 180° − 60° − 70° = 50°.

Classification by Angles

• Acute triangle: all three angles < 90°
• Right triangle: exactly one 90° angle
• Obtuse triangle: one angle > 90°
• Equiangular: all angles = 60° (same as equilateral)

Classification by Sides

• Scalene: all sides different lengths
• Isosceles: at least two sides equal
• Equilateral: all three sides equal (all angles 60°)

Exterior Angle Theorem

An exterior angle of a triangle equals the sum of the two non-adjacent interior angles. If exterior angle D is at vertex C, then D = A + B.