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The sum of three angles around a point, 2x, x, and x, equals 360 degrees, leading to the solution x = 90 degrees.

To find the unknown interior angle x, the exterior angle theorem was used, setting up and solving an equation to find x = 40 degrees.

The provided text contains a series of math problems, including algebraic expressions, exponents, fractions, and polynomial operations. The solutions demonstrate various techniques for simplifying and manipulating these expressions, such as factoring, expanding, and applying the rules of exponents and fractions.

The function f(x,y) = -2x^2 + 3xy^2 - 3y^2 + 4 has a local maximum value of 4 at (0,0).

The solution determines the Fourier coefficients for a periodic square pulse with a width of 3 and period of 12, finding the values of α, β, and λ in the given formula for ak.

The derivative of tan(θ) with respect to θ is sec^2(θ), derived using right-angled triangles and the definition of the derivative.

The provided examples demonstrate the continuity of functions at specific points. Polynomials are continuous everywhere, functions with undefined points are not continuous at those points, and absolute value functions are continuous everywhere, including at points where the expression inside the absolute value is zero.

The double integral, using polar coordinates and integration by parts, evaluates to π(e^2 + 1).

Roulette outcomes are random and independent, making future predictions impossible based on past results. Each number has an equal probability of appearing.

The solution to the system of linear equations is x = 1, y = -2, z = 3, and w = 2.