[math]\angle DCG[/math] and [math]\angle DBG[/math] are [b][u]opposite angles[/u][/b] of quadrilateral BDCG. Notice that these two angles are supplementary. Move vertices B, D, C, and G to see that this relationship is always true of opposite angles.[br][br]Using what you know about inscribed angles and circles, why do you think that opposite angles of a quadrilateral must always be supplementary?