Answer:
[tex]arc\ DE=39^o[/tex]
Step-by-step explanation:
step 1
Find the value of w
we know that
[tex]m\angle APB+m\angle APE=180^o[/tex] ---> by supplementary angles (form a linear pair)
substitute the given values
[tex](4w+8)^o+(4w+4)^o=180^o[/tex]
[tex]8w=180-12\\8w=168\\w=21[/tex]
step 2
Find the measure of angle EPD
we know that
[tex]m\angle APB=m\angle EPD+m\angle DPC[/tex] ----> by vertical angles
substitute
[tex](4w+8)^o=m\angle EPD+(2w+11)^o[/tex]
substitute the value of w
[tex](4(21)+8)^o=m\angle EPD+(2(21)+11)^o[/tex]
[tex]92^o=m\angle EPD+53^o[/tex]
[tex]m\angle EPD=92^o-53^o=39^o[/tex]
step 3
Find the measure of arc DE
we know that
[tex]arc\ DE=m\angle EPD[/tex] ----> by central angle
therefore
[tex]arc\ DE=39^o[/tex]
