You should add 5x+40 to 2(2x+20) and x, to see if they come up to 360. If they do, AC is a diamater of the circle.
So, let’s begin.
5x+40 + 2(2x+20) + x = 360
We need to take care of the brackets first.
5x+40 + 4x+40 + x = 360
Now, we will group the parts of the equation. We will put the unknown parts on the left, and the known ones on the right.
5x + 4x + x = 360 - 40 - 40
From here on it’s pretty straight-forward.
10x= 280
Divide both sides by 10.
x=28
Moving on,
5x+40 + 2(2x + 20) + x = 360
5*28 + 40 + 2(2*28 + 20) + 28 = 360
140 + 40 + 2(56 + 20) + 280 = 360
180 + 112 + 40 + 28 = 360
360 = 360
They are equal, therefore AC is a diamater of the circle.
