1. The basic formulas involving angles typically come from geometry and trigonometry. 2. The sum of angles in a triangle is always $$180^\circ$$, so for a triangle with angles $A$, $B$, and $C$, we have $$A + B + C = 180^\circ$$. 3. Complementary angles are two angles that add up to $$90^\circ$$, so if $\theta$ and $\phi$ are complementary, then $$\theta + \phi = 90^\circ$$. 4. Supplementary angles add up to $$180^\circ$$, so if $\alpha$ and $\beta$ are supplementary, then $$\alpha + \beta = 180^\circ$$. 5. For right triangle trigonometry, the basic ratios are: - $$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$ - $$\cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}$$ - $$\tan \theta = \frac{\text{opposite}}{\text{adjacent}}$$ 6. The laws of sines and cosines also connect angles and sides: - Law of sines: $$\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$$ - Law of cosines: $$c^2 = a^2 + b^2 - 2ab \cos C$$ These formulas cover many common uses of angles in geometry and trigonometry.