Question

What is the arc measure of abc in degrees

Answer 1

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°