To find the measure of arc EBC, we can use the relationship between the arcs and the diameters in a circle.
Since AC and BE are diameters of the circle, they divide the circle into two equal halves. The total measure of a circle is 360 degrees. When AC and BE intersect, they create four arcs: ADB, BEC, CDA, and EDC.
Given that the measure of arc DC is 50 degrees, we can find the measure of arc DAB (which is the rest of arc DC around the circle). Since arcs DC and DAB together make up one complete semicircle, we have:
Arc DAB = 180 degrees (since AC is a diameter)
Now we can find measure of arc DAB:
Measure of arc DAB = 180 – 50 = 130 degrees.
Next, since BE is also a diameter and bisects the circle, the measure of arc EBC will be equal to arc DAB due to the symmetry of the circle.
Thus, the measure of arc EBC is:
Arc EBC = 130 degrees.
In conclusion, the measure of arc EBC is 130 degrees.