For once, I was able to solve a problem. For this particular one, you have to use a combination of algebra and geometry, but this problem is absurdly easy compared to the usual slate of challenges I've tried to solve from this guy's channel.
Thursday, February 02, 2023
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Solution: start with the triangle at the top. As you see, all sides are congruent, so that makes it an equilateral. The interior angles of an equilateral are all 60 degrees. The top vertex of the larger triangle, being a vertical angle with the equilateral's, must therefore also be 60 degrees. The [9x-2] and [7x-6] angles have vertical angles inside the larger triangle as well. The sum of any triangle's interior angles will always be 180 degrees, so we now know the initial equation:
[7x-6] + [9x-2] + 60 = 180
Just solve from there, and you get
x = 8.
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