Question

Kite DCFE is inscribed in circle A

If the measure of arc DEF is 232°, what is the measure of ∠DEF?

Numerical Answers Expected!

Answer 1

Arc DEF = 232 degrees. So, arc DCF = 360-232 = 128. Now you use the director theorem and you do 128/2 = 64 degrees.


64 degrees is your answer

Answer 2

Answer:
`64^(\circ)`

Explanation:

Since, measure of arc DEF is 232°

By the given diagram,

`m\angle DAF = 360^(\circ) - arc ( m\angle D EF )`

⇒
`m\angle DAF = 360^(\circ) - 232^(\circ) = 128^(\circ)`

But by the central angle theorem,

`m\angle D EF = (m\angle DAF)/(2)`

⇒
`m\angle D EF = (128)/(2)=64^(\circ)`