Answer:
Part 1) [tex]arc\ AC=33\°[/tex]
Part 2) [tex]arc\ BC=130\°[/tex]
Step-by-step explanation:
Part 1) What is the measure of AC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<ABC=\frac{1}{2}(arc\ AC)[/tex]
substitute the values and solve for x
[tex]2.5x+4=\frac{1}{2}(7x-2)[/tex]
[tex]5x+8=(7x-2)[/tex]
[tex]7x-5x=8+2[/tex]
[tex]2x=10[/tex]
[tex]x=5\°[/tex]
Find the measure of arc AC
[tex]arc\ AC=7x-2=7(5)-2=33\°[/tex]
Part 2) What is the measure of BC ?
we know that
The inscribed angle is half that of the arc it comprises.
so
[tex]m<BDC=\frac{1}{2}(arc\ BC)[/tex]
substitute the values
[tex]65\°=\frac{1}{2}(arc\ BC)[/tex]
[tex]2*65\°=(arc\ BC)[/tex]
[tex]arc\ BC=130\°[/tex]
