Given equation of one side and opposite point, find the equation of the other two sides of triangle

Question

The vertex of an equilateral triangle is (2,3). The equation to the opposite side is x+y=2. Find the equation to the other two sides.

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Answer 1

The slope of the line $x + y = 2$ is $-1$ which forms a 45-degree angle with the x-axis. Therefore, the slopes of the other two sides must be $\tan{75°}$ and $\tan{15°}$. (Sorry for the atrocious drawing, but you get the idea)

Because the lines go through the point $(2,3)$, their line equations must be:

$$ y-3=\tan{75°}(x - 2)\\ y-3=\tan{15°}(x - 2) $$