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Kite DCFE is inscribed in circle A

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

Numerical Answers Expected!

Kite DCFE is inscribed in circle A If the measure of arc DEF is 232 what is the measure of DEF Numerical Answers Expected class=

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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:  [tex]64^{\circ}[/tex]

Step-by-step explanation:

Since, measure of arc DEF is 232°

By the given diagram,

[tex]m\angle DAF = 360^{\circ} - arc ( m\angle D EF )[/tex]

⇒ [tex]m\angle DAF = 360^{\circ} - 232^{\circ} = 128^{\circ}[/tex]

But by the central angle theorem,

[tex]m\angle D EF = \frac{m\angle DAF}{2}[/tex]

⇒ [tex]m\angle D EF = \frac{128}{2}=64^{\circ}[/tex]

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