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We’re given a diagram of a triangle.
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And we’re asked to find the value of 𝑥.
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And if you look at the diagram, you’ll see that all three of the angles in this triangle are expressed in terms of this unknown variable 𝑥.
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So, thinking about how to approach this problem, we need the key fact about angles in a triangle.
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And of course, it’s this, that the angles in a triangle sum to 180 degrees.
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So, think about how you can use this fact to help you answer this problem.
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Well, we don’t know what the values of the angles are, in terms of their numeric measures, but we do know them in terms of this unknown letter 𝑥.
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So, we can start writing an equation.
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So, if I add up all of the different angles in this triangle.
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So, that will be 𝑥 plus two 𝑥 minus 10 plus 𝑥 plus 30, if I add them altogether, it has to give me 180 degrees.
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So, here is an equation, or the beginning of an equation, that I can use to work out this letter 𝑥.
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So, the next thing I’d want to do is to simplify this equation.
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If I look at the left-hand side, I’ve got 𝑥 plus two 𝑥 plus 𝑥, so I’ve got four 𝑥 overall.
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And then, I’ve got minus 10 plus 30, so overall, I’ve got plus 20.
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So, simplifying this equation, I have four 𝑥 plus 20 is equal to 180.
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Now, I want to solve this equation.
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So, the first step is gonna be to subtract 20 from both sides.
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And when I do, I get four 𝑥 is equal to 160.
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Next, to work out the value of 𝑥, I need to divide both sides of the equation by four.
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And when I do that, it gives me 𝑥 is equal to 40, which is therefore the answer to this question.
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So, this question involved using that fact about the angle sum in a triangle, but also some algebra skills, in terms of setting up and then solving an equation, in order to work out the value of this unknown letter 𝑥.