Question

CDEF is a cyclic quadrilateral. m∠CFE = 80°. m∠CEF = 45

a. What is the measure of ∠EDF?

b. Explain the steps you took to find the measure of ∠EDF.

Answer 1

Heya !!!!

here is your answer !!!

in the given figure :-

CDEF is cyclic Quadrilateral !!

now ,

so the

< FEC =< FDC { 45 ° }

( angle in same sagement )

hence ,

< FDC =45 ° ------------------(1)

NOW ,

< CFE + < CDE = 180 °

{ cyclic Quadrilateral }

80 ° + < FDC + < FDE = 180 °

< FDC + < FDE = 100 .

now , from equation 1 we have

< FDC = 45 °

45 °. + < FDE = 100 °

=> < FDE =100 - 45 °

=> < FDE = 55°

hence the Value of X = 55°

hope it helps you dear !!!

thanks !!!

Answer 2

Hi.

Good Question and Keep Progressing.

Here is your answer---

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For the Measure of ∠EDF

In ΔCFE,
     
  ∠ FCE + ∠ CFE + ∠ CEF = 180°      [ Angels Sum Property]
   
 ∠ FCE = 180° - (80° + 45°)
     
   ∠ FCE  = 180° - 125°
     
     ∠ FCE =  55°

Now, ∠ FCE = ∠ EDF        (Angels on the Same Segments are equals.)
                     = 55°

Thus, the measure of the ∠ EDF is 55°.

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Hope it helps.

Have a nice day.