The arc that an inscribed angle forms is twice the amount of degrees as the inscribed angle. Knowing this we can see that Angle BCD is an insribed angle and its corresponding arc is Arc BD. We can apply our knowledge and multiply the measure of Angle BCD by 2 to get Arc BD.
This can be written out as-
2(87)=174
So now we know the measure of Arc BD is 174 degrees. We can then subtract the measure of Arc BD (174°) by Arc BE (76°) to get the measure of Arc DE which can be written as:
174-76=98
Measure of Arc DE=98°