CharlesGSE
z = 360-2(x+a)-2(y+b) = 2*[180-(a+b)]-2(x+y), and z = 180-(a+b)So, z = 2z - 2(x+y)
=> z = 2 (x+y)[/color]
So, x is dependednt on both x & y. Hence, C.
Hey,
Could you explain why do you have like z = 360-2(x+a)-2(y+b) = 2*[180-(a+b)]-2(x+y) ?
I tried to use the rule angle (ABC) = 1/2angle (AOC) with A and C on the cord but it doesn't work... Ty
CharlesGSEHi Charles,
All the smaller triangles in the graph are isosceles triangles. This is because all of them have two sides as the radius of the circle. Hence a = b in that drawing.
If we look at the biggest triangle, the angles added up are a + a + x + x + y + y = 180. We also have z = 180 - 2a so we can replace 2a with 180 - z.
Finally we get (180 - z) + 2x + 2y = 180, z = 2x + 2y. (which is exactly your ABC = 1/2 (AOC) theorem, which is x + y = 1/2 * z)
Therefore we need both x and y to calculate z, and we choose C.