In the figure below, AC and BE are diameters of circle P. What is the arc measure of DE in degrees?

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°

rounding to the nearest thousandth would be 452,000