Answer:
arc DE = 39°
Step-by-step explanation:
Since BE is a diameter then
∠ BPA + ∠ EPA = 180° ( straight angle ), substitute values
4w + 8 + 4w + 4 = 180, that is
8w + 12 = 180 ( subtract 12 from both sides )
8w = 168 ( divide both sides by 8 )
w = 21
Since AC is a diameter, then
∠ EPA + ∠ EPD + ∠ DPC = 180° ( straight angle ), substitute values
4w + 4 + ∠ EPD + 2w + 11 = 180, that is
6w + 15 + ∠ EPD = 180, substitute w = 21
6(21) + 15 + ∠ EPD = 180
126 + 15 + ∠ EPD = 180
141 + ∠ EPD = 180 (subtract 141 from both sides )
∠ EPD = 39°
The angle at the centre of the circle is equal to the arc subtending it, that is
arc DE = ∠ EPD = 39°
