Question

Kite DCFE is inscribed in circle A shown below.

If the measure of is 248°, what is the measure of ∠DEF?

Answer 1

Measure of what is 248? :P

Answer 2

sorry arc DEF

Answer 3

Okay :-) So you know awhole circle is 360, so to find the remaining length of the arc is 360-248.
112.
Now, a relation between an arc and an angle is that the arc is two times the angle, so take 112 and divide by 2.
56.

Answer 4

oh ok that makes sence
thank you :)

Answer 5

FLVS?

Answer 6

?

Answer 7

Oh god ranga is here, I must've done it wrong!

Answer 8

lol

Answer 9

This is a cyclic quadrilateral where the four corners are all in a circle. In a cyclic quadrilateral the opposite angles add to 180 degrees.

If arc DEF = 248 then DCF = half of arc DEF = 248/12 = 124

DEF + DCF = 180. DCF = 124. Solve for DEF.

Answer 10

so i do 248+124+180

Answer 11

ohhhhh nevermind

Answer 12

so it is 56

Answer 13

DEF + DCF = 180
DCF = 124
DEF + 124 = 180
DEF = 180 - 124 = 56

Yes your answer is correct.

Answer 14

ok thank you boys

Answer 15

We use two theorems here: Inscribed angle theorem and opposite angles of a cyclic quadrilateral add to 180 degrees.

Answer 16

you are welcome.