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°