Answer:
x = 12
Step-by-step explanation:
Vertical angles are congruent, so ...
4x = 48°
x = 12° . . . . . . divide by 4
The vertices of the triangle are the points where any pair of lines intersect.
We start by setting up the system
![\begin{cases}y=-x+2\\y=2x-1 \end{cases} \iff -x+2=2x-1 \iff 3x=3 \iff x=1](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3D-x%2B2%5C%5Cy%3D2x-1%20%5Cend%7Bcases%7D%20%5Ciff%20-x%2B2%3D2x-1%20%5Ciff%203x%3D3%20%5Ciff%20x%3D1)
Using one of the two equations we can derive the correspondent y value:
![f(x)=-x+2 \implies f(1)=-1+2 = 1](https://tex.z-dn.net/?f=f%28x%29%3D-x%2B2%20%5Cimplies%20f%281%29%3D-1%2B2%20%3D%201)
So, one vertex is (1, 1)
We choose the other two pairs of lines to find the other vertices:
![\begin{cases}y=-x+2\\y=x-2 \end{cases} \iff -x+2=x-2 \iff x=2 \implies y = 0](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3D-x%2B2%5C%5Cy%3Dx-2%20%5Cend%7Bcases%7D%20%5Ciff%20-x%2B2%3Dx-2%20%5Ciff%20x%3D2%20%5Cimplies%20y%20%3D%200)
![\begin{cases}y=x-2\\y=2x-1 \end{cases} \iff x-2=2x-1 \iff x=-1 \implies y=-3](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7Dy%3Dx-2%5C%5Cy%3D2x-1%20%5Cend%7Bcases%7D%20%5Ciff%20x-2%3D2x-1%20%5Ciff%20x%3D-1%20%5Cimplies%20y%3D-3)
So, the three vertices are (1, 1), (2, 0), (-1, -3).
20% = 0.20.2 * 1630 = 326