In the given figure, what is the value of 𝑥? A) 40, B) 105, C) 100, or D) 120.
So this given figure will be considered a four-sided polygon. And here, we’re trying to find the value of 𝑥. And 𝑥 is an angle measure, which is measured in degrees. Well, how many degrees are inside of a four-sided polygon? That would be 360 degrees. There is a formula to find this number, 360. We take the number of sides of the shape, subtract two, and then multiply by 180. There are four sides. And four minus two is two. And two times 180 is how we get our 360 degrees.
Now, let’s say we’re not good at remembering formulas. A useful way to find the number of degrees inside of a shape is to use triangles, because most of us will remember that a triangle is 180 degrees. Well, how many triangles fit inside the shape? We need to draw a line from one corner to the other. And there are a few options we have. Let’s say we drew the line here. So this would create two triangles. So again, two times the 180 degrees in each triangle would give us 360 degrees. So why is this even useful? Well, if we add each angle measure together, we can set that equal to 360 degrees. So we add the three 𝑥s together. And then we add 60 and then set it equal to 360. Again, we’re adding each angle measure together and setting it equal to the total number of degrees inside of this four-sided polygon.
So on the left-hand side, we can combine like terms. 𝑥 plus 𝑥 plus 𝑥 is three 𝑥. Now, we need to subtract 60 from both sides of the equation. And we are left with three 𝑥 equals 300, because 360 minus 60 is 300. And then, the 60s cancel on the left-hand side. So now, we divide both sides of the equation by three and find that 𝑥 is equal to 100. So each of these angles are 100 degrees.
So once again, the value of 𝑥 would be 100, making C our answer.