Question

My apologies. Would I be able to receive assistance for numbers 2, 4, and 5 on this sheet? (Algebra 2)

Answer 1

I'll try to detail as much as possible the solution to exercise 2. Exercises 4 and 5 and basically identical: you'll have to set up a system translating the sentences to equations, and solve it. Please try to solve exercises 4 and 5 on your own (that's when you really learn!!) by mimicking how I solved exercise 2.

Let's call the three angles
`s,\ m,\ l` (small, medium and large, respectively). The first sentence translates to

`l = s+m+10`

The second sentence translates to

`l = 3s-10`

Since we have three unknowns, we need a third equation: this equation is implicit, because we know that the sum of the angles of a triangle is always 180 degrees:

`s+m+l=180`

So, we have the following system (rearranged in standard form):

`\begin{cases} s+m-l = -10\\3s-l = 10\\s+m+l=180\end{cases}`

If you subtract the first equation from the third you get

`(s+m+l)-(s+m-l) = 180-(-10) \iff 2l = 190 \iff l = 95`

Plug this value for
`l` in the second equation:

`3s-l = 10 \iff 3s - 95 = 10 \iff 3s = 105 \iff s = 35`

Finally, complete to 180 to compute
`m`:

`s+m+l=180 \iff 35+m+95 = 180 \iff m = 180-35-95 = 50`

So, the angles are 35, 50 and 95 degrees