Angles and Polygons

Angle pairs

Complementary angles

∠ A + ∠ B = 90^{\circ}

Supplementary angles

∠ A + ∠ B = 180^{\circ}

Vertical angles

∠ A = ∠ B

Corresponding angles

equal

Alternate interior angles

equal

Alternate exterior angles

equal

Same-side interior angles

sum to 180^{\circ}

Sum of interior angles

S = (n - 2) \times 180^{\circ}

Each interior angle, regular

\frac{(n - 2) \times 180^{\circ}}{n}

Sum of exterior angles

360^{\circ}

convex polygon

Each exterior angle, regular

\frac{360^{\circ}}{n}

Number of diagonals

\frac{n (n - 3)}{2}

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