Question

In the figure below, CE and AB are parallel and CE is the bisector of angle ACD. If angle ACD measures 110 degrees, what is the measure of arc BC?

Answer 1

ECD=ECA=55 degrees (ACD is bisected)
ECA=BAC=55 (opposite interior angles)
hmm.. how to get an arc length without a radius...???

Answer 2

The measure of an arc is EITHER the length of the arc, OR the angle subtended at the centre of the circle. We know from the answer above that angle BAC = 55, so the angle at the centre is twice this, or 110. This is the measure of the arc BC. Do you remeber the theorem that the angle at the centre is twice the angle at the circumference?

Answer 3

No I had forgotten, though I figured there was some rule like that. Thanks.