Question

M∠A=(x+45)°,
mKE =(x+20)°,
mEW=(3x)° ,
Find: mKW.

Answer 1

The measure of the arc KW is
`160\°`

Explanation:

we know that

The inscribed angle measures half that of the arc comprising

so

`m<A=(1)/(2)(arc\ KE+arc\ EW)`

substitute the values and solve for x

`(x+45)\°=(1)/(2)(x+20+3x)\°`

`(2x+90)\°=(4x+20)\°`

`4x-2x=90\°-20\°`

`2x=70\°`

`x=70\°/2=35\°`

Find the measure of the arc KW

`arc\ KW=(arc\ KE+arc\ EW)=(4x+20)\°`

substitute the value of x

`arc\ KW=4(35\°)+20\°=160\°`