Respuesta :

Answer:

The measure of arc ABC is 283°.

Step-by-step explanation:

We know that the whole arc is equal to 360°, that means

[tex]AC+AB+BC=360[/tex]

Where [tex]AC=7y-7[/tex], [tex]AB=4y+6[/tex] and [tex]BC=20y-11[/tex]. Replacing these expressiones, we have

[tex]7y-7+4y+6+20y-11=360\\31y-12=360\\31y=360+12\\y=\frac{372}{31}\\y=12[/tex]

But, arc ABC is defined by the sum of arcs AB and BC:

[tex]ABC=AB+BC=4y+6+20y-11=24y-5=24(12)-5=283[/tex]

Therefore, the measure of arc ABC is 283°.

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Chrisnando

Answer:

Arc measure of ABC is 283°

Step-by-step explanation:

We know the total angle of the circle is 360°.

Therefore,

(20y - 11) + (4y +6) + (7y - 7) = 360°

Collecting like terms, we have:

20y + 4y + 7y = 360 + 7 - 6 + 11

31y = 372

Let's divide both sides by 31.

[tex] \frac{31y}{31} = \frac{372}{31} [/tex]

y = 12

The arc measure of ABC is the sum of AB and BC. To find the arc measure of ABC, we have:

(4y +6) + (20y - 11)

Collecting like terms, we have:

4y + 20y + 6 - 11

24y - 5

Let's substitute 12 for y

24(12) - 5

288 - 5 = 283°

Arc measure of ABC is 283°

Ver imagen Chrisnando

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