First of all I want to point out you drew the diagram a little wrong. The Arc is 41 doesn't mean its 41 degrees it means it has length 41 so remove the degrees symbol.
Now for the answer the other arc have to have angle 40 too because vertical angles. And because the radius is the same, both of the length has formula 40/360*pi*2*radius which is 41 in this case. So x has to be 41 also :) Done!
D a theorem needs to be proven
Yes she will have enough. Here is why.
10 1/8 x 13 3/4 = 139
Therefore the room is 139 square feet. She has 150 square feet of carpet, so she has enough.
