Answer:
Arc measure DBE is 321 degrees.
Step-by-step explanation:
Since BE is a diameter of circle P, (4w+8)+(4w+4)=180. You can use this to figure out what w is.
<em>(4w+8)+(4w+4)=180</em>
<em>4w+8+4w+4=180</em>
<em>8w+12=180</em>
<em>8w=168</em>
<em>w=21</em>
This means arc measure BA is 4(21)+8 degrees, which is 92 degrees. Since arc measures BA and CE are vertical angles, CE is also 92. Then 92-(2w+11)=DE, and 360 - DE = DBE.
<em>DE=92-(2w+11)</em>
<em>DE=92-2(21)-11</em>
<em>DE=92-42-11</em>
<em>DE=39</em>
<em />
<em>DE+DBE=360</em>
<em>39+DBE=360</em>
<em>DBE=321</em>
<em />
Therefore, the arc measure of DBE is 321 degrees!
(I filled it in the real problem and it says it is correct so this should be right.)
