Answer:
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
Answer: m(arc)ED = 39 degrees
