Complement of Theta.

I don't think there are any preferred symbols. People use whatever Greek letters they like best. α, β, γ are frequently used, for example.
In physics a glancing angle (the angle between an incident beam and the surface upon which it is incident) is often denoted by θ (theta).

There is no standard delineation for the angles of a triangle as long as it is clear and not liable to be confused with others within the particular case; though some of the Greek letters are conventional for certain applications.

Common ones are -


Δ and δ - the Differentiation operators,

π That wonderfully poetically-described "irrational and transcendental number" Pi, crops up all over the place, not just in simple circle and sphere sums!

Σ is capital-Sigma, the series / summation operator, with superscript / subscript limit notes,

λ and σ are Lambda and Rho, conventionally used for wavelength and density respectively, in fields such as Acoustics,

α, β and γ are used to denote the alpha, beta and gamma forms of radioactivity. Gamma might just show here as an italic 'y',

Ω - Omega, for Ohms, of electrical resistance,

ω - lower-case omega, used in calculations of rotation.

The symbol for theta is Θ in caps and θ in small.
The small θ is often used for acute angles as a first choice. The other angles are then denoted with alpha, beta or gama.

I don't think it a hard and fast rule. Just habit, the way n is used to denote a random number. Or x and y used for algebra.

Your reference to theta for right angles triangles specifically is perhaps due to trigonometry where sin θ, cos θ and tan θ are most common.