tm123mis
contestada

Kite DCFE is inscribed in circle A shown below.



If the measure of arc DEF is 248°, what is the measure of ∠DEF?

Kite DCFE is inscribed in circle A shown below If the measure of arc DEF is 248 what is the measure of DEF class=

Respuesta :

lublana

Answer:

[tex]\angle[/tex]DEF=[tex]56^{\circ}[/tex]

Step-by-step explanation:

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

The measure of arc DEF=[tex]248^{\circ}[/tex]

We have to find the measure of angle DEF.

arc DCF=360-arcDEF=360-248=[tex]112^{\circ}[/tex]

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, [tex]\angle[/tex] DEF=[tex]\frac{1}{2}\times[/tex]arcDCF

[tex]\angle[/tex]DEF=[tex]\frac{1}{2}\times 112=56^{\circ}[/tex]

Hence, the measure of angle DEF=56 degrees.

Answer:[tex]\angle[/tex]DEF=[tex]56^{\circ}[/tex]

A circle is a curve sketched out by a point moving in a plane. The measure of the ∠DEF is 56°.

What is a circle?

A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.

As it is given that the measure of the arc DEF is 248°, therefore, the measure of the arc DCF can be written as,

[tex]arcFED + arcDCF = 360^o\\\\248^o +arc DCF = 360^o\\\\arcDCF = 112^o[/tex]

As the measure of arc DCF is 112°, therefore the measure of ∠DAF will be 112°. Now, since the angle formed by arc DCF at the centre of the circle is 112°, therefore, the measure of the ∠DEF will be half of this.

[tex]\angle FED = \dfrac{arc DCF}{2} = \dfrac{112^o}{2}=56^o[/tex]

Hence, the measure of the ∠DEF is 56°.

Learn more about Circle:

https://brainly.com/question/11833983

#SPJ3

Otras preguntas