Question

Circle P is below. What is the arc measure of ABC in degrees

Answer 1

Step-by-step explanation:

$\bf \huge \: Question \:$

• Circle P is below. What is the arc measure of ABC in degrees

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$\bf \huge \: </strong><strong>Given</strong><strong> \:$

• APB = (4y+6)°
• APC = (7y-7)°
• BPC = (20y − 11)°

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$\bf \huge \: To \:Find$

• What is the arc measure of ABC in degrees

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$\bf\: we\: Know\: That$

$\bf\:The \: sum\: of \: the \: arc \: angles\: is\red{ 360°.}$

Putting the value of all sums

$\bf\:7y − 7 + 4y + 6 + 20y − 11 = 360$

$\bf\:31y − 12 = 360$

$\bf\:31y = 360+12$

$\bf\:31y = 372$

$\bf \: y = \frac{272}{31}$

$\bf\red{y = 12}$

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The measure of arc ABC is the sum of arcs AB and BC...

Then putting the value

$\bf\:4y + 6 + 20y − 11$

$\bf\:= 24y − 5$

Putting the value of y

$\bf\:= 24(12) − 5$

$\bf \:On\: multiplying$

$\bf\red{= 283}$

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Answer 2

Answer:

4y +6 + 7y -7 + 20y -11 = 360°

31 y - 12 = 360

31 y = 360 + 12

31 y = 372

y = 372/31

y = 12

putting the value of y ,

• 4(12)+6 = 48+6 = 54
• 7(12 ) -7 = 77
• 20( 12 ) -11 = 229

229 + 54 = 283