Question

in circle o, $overline{ac}$ and $overline{be}$ are diameters. the measure of arc dc is 50°. what is the measure of $overline{ebc}$? 40° 90° 140° 220°

Explanation:

Step1: Recall circle - arc properties

The measure of a full - circle arc is 360°. Since $\overline{AC}$ and $\overline{BE}$ are diameters, $\angle EOC = 90^{\circ}$ and $\angle DOC=50^{\circ}$.

Step2: Calculate the measure of arc $\overset{\frown}{EBC}$

The measure of arc $\overset{\frown}{EBC}=\angle EOC+\angle DOC + 180^{\circ}-\angle EOD$. Since $\angle EOC = 90^{\circ}$ and $\angle DOC = 50^{\circ}$, and $\angle EOD=90^{\circ}-50^{\circ}=40^{\circ}$, then the measure of arc $\overset{\frown}{EBC}=90^{\circ}+50^{\circ}+90^{\circ}=220^{\circ}$.

Answer:

D. 220°