Question

Chord CK is the diameter of circle O. m arc JC=(19x)degrees and m arc JK=(9(x+2)-6)degrees.

What is the value of X?

Answer 1

What is the value of arc CK?

Answer 2

Wouldn't that be half the circle? If so 180 right.

Answer 3

That is correct.. and we know by looking at the drawing that arc JC and arc JK make up arc CK...So the equation would look like ARC JC + ARC JK = ARC CK (or 180 deg)..now substitur the values for JC and JK and you can solve.

Answer 4

Ok hang on

Answer 5

Ok if I have this right, arc CJ is 19x degrees and arc JK is 9(x+2)-6. Is that right? If it's not, please correct me, but I am going to go on as if it is correct, and we will adjust it accordingly if not. Ok, the first thing we have to remember is that the diameter splits the circle in half, and that each half is a semicircle which measures 180 degrees. So if arc CJK is a semicircle, its measure is 180, right? So that means that the measure of CJ and JK add up to = 180. (19x) + [9(x+2)-6] = 180. Distributing the 9 into the (x+2) gives us the term to be 9x + 18 - 6 which is 9x + 12. Now add that to the 19x to get 28x - 6 = 180. Add 6 to both sides to get 28x = 186. Divide 186 by 28 and get x = 6.64. That seems a little weird, like maybe I did misinterpret your value for arc JK. But regardless, that's the way you do it, and yes, arc CLK is 180.

Answer 6

Yup I got 6

Answer 7

Winner winner chicken dinner..6 is correct

Answer 8

Lol thanks for the help!