Question

Farial inscribed a quadrilateral ABCD in a circle, as shown below.



If the measure of arc BCD is 220°, what is the measure of angle BCD?

Answer 1

angle BCD = 1/2 arc BAD

Answer 2

?

Answer 3

Angle BCD is an inscribed angle of a circle and has measure half that of its intercepted arc. As shown, Angle BCD has measure 70.
Another way to do the problem is to remember that when a quadrilateral is inscribed in a circle, opposite angles of the quadrilateral are supplementary.
Angle A cuts off arc BCD which has measure 220. So angle BCD = 1/2 of 220 = 110.
The angle whose measure about which the problem asks is oppposite the 110 angle. So, it has measure 70.