Question

Kite DCFE is inscribed in circle A shown below.

Answer 1

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°

Answer 2

Answer:

$\angle$DEF=$56^{\circ}$

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=$\frac{1}{2}\times$arcDCF

$\angle$DEF=$\frac{1}{2}\times 112=56^{\circ}$

Hence, the measure of angle DEF=56 degrees.

Answer:$\angle$DEF=$56^{\circ}$