Video: Solving Equations That Represent the Measure of Angles in the Same Triangle

Find the value of 𝑥.

02:00

Video Transcript

We’re given a diagram of a triangle. And we’re asked to find the value of 𝑥. 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.

So, thinking about how to approach this problem, we need the key fact about angles in a triangle. And of course, it’s this, that the angles in a triangle sum to 180 degrees. So, think about how you can use this fact to help you answer this problem. 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.

So, we can start writing an equation. So, if I add up all of the different angles in this triangle. 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. So, here is an equation, or the beginning of an equation, that I can use to work out this letter 𝑥.

So, the next thing I’d want to do is to simplify this equation. If I look at the left-hand side, I’ve got 𝑥 plus two 𝑥 plus 𝑥, so I’ve got four 𝑥 overall. And then, I’ve got minus 10 plus 30, so overall, I’ve got plus 20. So, simplifying this equation, I have four 𝑥 plus 20 is equal to 180. Now, I want to solve this equation. So, the first step is gonna be to subtract 20 from both sides. And when I do, I get four 𝑥 is equal to 160.

Next, to work out the value of 𝑥, I need to divide both sides of the equation by four. And when I do that, it gives me 𝑥 is equal to 40, which is therefore the answer to this question. 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.

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