find the measure for O?

The arc intercepted by the 71 degree angle is 2(71) = 142 degrees.

Since part of this arc is 104 degrees, the other part is the "C" degrees.

Therefore 142 - 104 = 38 degrees...and that is the measure of "C."

Likewise the arc intercepted by the 68 degee angle is 2(68) = 136 degrees.

Then,  the remaining minor arc - "B" - between the 71 degree angle and the 68 degree angle is just 360 - 136 - 104 = 120 degrees.  Therefore "A" = (1/2)(120 + 104) = (1/2)(224) = 112 degrees.

BTW......nice pic, Melody !!!

Is 104 degrees and C and B degrees the angles from the centre that subtend to those arcs?

What is O?

I do not understand what you are asking.

I still don't know what you want but

A=180-68=112 degrees  (opp angles in cyclic quad are supplementary)

104+C=2*71 = 142  (the angle at the centre = 2* angle at the circumference when both are subtended from the same arc.

C=142-104=38 degrees

If I scribbled down the correct numbers here on my scrap of paper i got B = 120 degrees (accuracy very questionable at this moment)

I still do not know what you actually want!

Maybe you just want all the angles at the centre.  I am a bit slow sometimes - i'm not much good at forensic mathematics.

Ok the last angle is just 360 degrees minus the other 3 angles.

continued

Thank you kind Sir.

tealftlove,

I sincerely hope that you wil be a lot more gracious with this question than you were with the other!

Melody.

You took points off me because I took the time to try and help you.

Here I have given you considerable help and still you offer no thanks or gratitude of any kind.

You are one of the rudest people who has ever been on this forum.

Let other people decide how gracious you are!

http://web2.0calc.com/questions/find-the-value-of-each-variable-for-each-circle-the-dot-represents-the-center_1