Inequalities with angles

Inequalities with angles are statements that compare the sizes of angles in geometric figures, often triangles or polygons. These inequalities can help us understand how the angles relate to the sides or other elements of the figure.

Important properties

• In any triangle, the sum of the angles is 180°.

• In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

• The triangle inequality for angles: In any triangle, the measure of any angle is less than the sum of the other two angles.

• Exterior angle inequality: An exterior angle of a triangle is greater than either of the two non-adjacent interior angles.