What is the arc measure of arc (DE) in degrees?

m(arc)ED = 39 degrees

Step-by-step explanation:

The measure of an arc of a circle is equal to the measure of the central angle that intercepts it.

BE is a diameter. That means that m<BPE = 180.

AC is a diameter. That means that m<APC = 180.

Let's start with angle BPE to find w:

m<BPE = m<BPA + m<EPA = 180

4w + 8 + 4w + 4 = 180

8w + 12 = 180

8w = 168

w = 21

Now we deal with angle APC:

m<APC = m<APE + m<EPD + m<DPC = 180

4w + 4 + m<EPD + 2w + 11 = 180

6w + 15 + m<EPD = 180

m<EPD + 6w = 165       Equation 1

Now we use w = 21 in Equation 1.

m<EPD + 6w = 165

m<EPD + 6(21) = 165

m<EPD + 126 = 165

m<EPD = 39

Since the arc measure equals the measure of the central angle that intersects it, m(arc)ED = 39 degrees

m(arc)ED = 39 degrees