Answer:
The measure of the arc KW is [tex]160\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<A=\frac{1}{2}(arc\ KE+arc\ EW)[/tex]
substitute the values and solve for x
[tex](x+45)\°=\frac{1}{2}(x+20+3x)\°[/tex]
[tex](2x+90)\°=(4x+20)\°[/tex]
[tex]4x-2x=90\°-20\°[/tex]
[tex]2x=70\°[/tex]
[tex]x=70\°/2=35\°[/tex]
Find the measure of the arc KW
[tex]arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°[/tex]
substitute the value of x
[tex]arc\ KW=4(35\°)+20\°=160\°[/tex]
