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.