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What is the arc measure of abc in degrees

What is the arc measure of abc in degrees-example-1

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Given:

The measure of arc AB is (4y + 6)°

The measure of arc BC is (20y - 11)°

The measure of arc AC is (7y - 7)°

We need to determine the measure of arc ABC.

Value of y:

The value of y is given by


m \widehat{AB}+m \widehat{BC}+ m \widehat{AC}=360

Substituting the values, we get;


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

Adding the like terms, we have;


31y-12=360

Adding both sides of the equation by 12, we have;


31y=372


y=12

Thus, the value of y is 12.

Measure of arc ABC:

The measure of arc ABC can be determined by adding the measure of arc AB and arc BC.

Thus, we have;


m \widehat{ABC}=m \widehat{AB}+ m \widehat{BC}


m \widehat{AB}+m \widehat {BC}=4y+6+20y-11


=24y-5

Substituting y = 12, we get;


m \widehat{AB}+m \widehat {BC}=24(12)-5


=288-5


m \widehat{AB}+m \widehat {BC}=283^(\circ)

Thus, the measure of arc ABC is 283°

User Jesper Palm
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