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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?


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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! class=

Verified Answer :

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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:  \(64^{\circ}\)

Step-by-step 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,

\(m\angle D EF = \frac{m\angle DAF}{2}\)

⇒ \(m\angle D EF = \frac{128}{2}=64^{\circ}\)

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