Math HELP with arcs!!?

Question

I dont get how to find the measure of an arc.
http://i15.photobucket.com/albums/a372/cowqtie101/mathgeo.jpg
I dont get why the answer to find the measure of arc BC is 54...and i dont get how to find the measure of angle ADB..HELP

Answer 1

An inscribed angle (where the angle touches the far side of the circle) intercepts an arc whose measure is equal to twice the measure of the angle. Angle BDC is 27 degrees, and point D is on the circle, so the measure of arc BC is 2*27 = 54 degrees.

You use the same process twice, once in reverse, to get angle ADB.

You are given that angle ACB is 50 degrees, and point C is on the circle... so the measure of arc AB must be 2*50 = 100 degrees. Angle ADB is a different inscribed angle that intercepts exactly the same arc. Since the measure of arc AB is 100 degrees, and point D is also on the circle, the measure of angle ADB must be half of the arc measure, or 50 degrees.

Answer 2

54 is not correct, if I understand the figure correctly.

The other contributors make the tacit assumption that ABCD is a rectangle, and that the two diagonals intersect at the center of the circle............

However, if this were the case, then
But since
This is unfortunate, since it means that EC, and
Tell you teacher exactly that; "E does not lie at the center of the circle."

He'll probable get a confused look on his face, think for a few minutes, and then, if has any worth as a teacher, give you some bonus points.....

Note: with the information given, it *is* still possible to calculate the length of arc BC; but without knowing beforehand the length of DB or EB, the calculations become quite complicated, and require an in-depth knowledge of trigonometry......

I'm pretty sure thats right.
Good luck,
~W.O.M.B.A.T.

Answer 3

An inscribed angle = (1/2)x(arc).

Arc BC = 2x27=54.

Arc AB = 2x(angle ACB) = 2x50=100

angle ADB = (1/2)x(arc AB) = (1/2)x100 = 50