Question

In the figure below, AC and BE are diameters of circle P.

Answer 1

Answer:

$arc\ DE=39^o$

Step-by-step explanation:

step 1

Find the value of w

we know that

$m\angle APB+m\angle APE=180^o$ ---> by supplementary angles (form a linear pair)

substitute the given values

$(4w+8)^o+(4w+4)^o=180^o$

$8w=180-12\\8w=168\\w=21$

step 2

Find the measure of angle EPD

we know that

$m\angle APB=m\angle EPD+m\angle DPC$ ----> by vertical angles

substitute

$(4w+8)^o=m\angle EPD+(2w+11)^o$

substitute the value of w

$(4(21)+8)^o=m\angle EPD+(2(21)+11)^o$

$92^o=m\angle EPD+53^o$

$m\angle EPD=92^o-53^o=39^o$

step 3

Find the measure of arc DE

we know that

$arc\ DE=m\angle EPD$ ----> by central angle

therefore

$arc\ DE=39^o$

Answer 2

Answer:

Step-by-step explanation:

39