Question

Kite DCFE is inscribed in circle A shown below.



If the measure of DEF is 266°, what is the measure of ∡DEF?

Answer 1

Wait, you're wanting to know the angle of DEF?

Answer 2

∡DEF is 266

Answer 3

i don't understand. given DEF and you wanna measure of ∡DEF?

Answer 4

The arch of DEF is 266

Answer 5

As far as I can tell, this question is saying "x is 5. What is x?"...

Answer 6

There are 360 degrees in a circle. If the great arc is 266, the rest of the circle is 360 - 266 = 94. Then, angle DEF is an inscribed angle intersecting that 94 degree arc, so it is then half of it.

Answer is 94/2 = 47

Answer 7

If arc DEF = 266 then arc DCF = 94

Join DA and FA

then angle DAF = 94..... angle standing on the arc DCF

then angle DEF = 47 angle at the centre is double the angle at the circumference standing on the same arc

Answer 8

Could have also done inscribed angle with ∡DCF to get it = to 133 and then opp angles of inscribed quad supp to find ∡DEC = 47

Answer 9

yep... DCF = 133 angle at the centre is double the angle at the circumference

DCFE is a cyclic quadrilateral (opposite angles spplementary

then DEF = 47