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kati45 [8]
3 years ago
15

What is the arc measure of abc in degrees

Mathematics
1 answer:
Virty [35]3 years ago
6 0

<u>Given</u>:

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.

<u>Value of y:</u>

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.

<u>Measure of arc ABC:</u>

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°

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