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A very useful result called the inscribed angle theorem tells us that, given any <em>inscribed angle</em> on a circle (an angle on the inside edge of a circle) the <em>central angle </em>that <em>subtends the same arc</em> is <em>twice the measure of the inscribed angle</em>. I've included a visual example for this problem if any of that vocabulary is unfamiliar.
Here, the inscribed angle ∠C = 87° is attached to the arc DEB. According to the inscribed angle theorem, the central angle swept out by DEB should then be 87 x 2 = 174°. To find the measure of arc DE, we note that arc DEB is just arc DE + arc EB. We're given that arc EB measures 76°, so we subtract that from 174 to find that arc DE = 174 - 76 = 98°
