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Alecsey [184]
3 years ago
5

Kite DCFE is inscribed in circle A shown below.

Mathematics
2 answers:
kogti [31]3 years ago
7 0

Answer:

∠DEF =56°

Step-by-step explanation:

We are given that arc DEF = 248°

So, arc DCF = 360°-248°

arc DCF = 112°

Now we are required to find the ∠DEF.

So, we will use Inscribed angle theorem.  

Inscribed angle theorem: The measure of an inscribed angle is equal to one-half the measure of its intercepted arc.  

Intercepted arc = arc DCF = 112°

Inscribed angle = ∠DEF

⇒∠DEF = \frac{1}{2}arcDCF

⇒∠DEF = \frac{1}{2}\times 112^{\circ}

⇒∠DEF =56°

Hence the measure of ∠DEF =56°

Blababa [14]3 years ago
5 0

Answer:

\angleDEF=56^{\circ}

Step-by-step explanation:

We are given that a kite DCFE is inscribed in a circle A.

The measure of arc DEF=248^{\circ}

We have to find the measure of angle DEF.

arc DCF=360-arcDEF=360-248=112^{\circ}

Because complete angle =360 degrees

Inscribed angle theorem:It states that inscribed angle is equal to half of the measure of its  intercepted arc.

Therefore, \angle DEF=\frac{1}{2}\timesarcDCF

\angleDEF=\frac{1}{2}\times 112=56^{\circ}

Hence, the measure of angle DEF=56 degrees.

Answer:\angleDEF=56^{\circ}

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