Question

Given: m∠MEJ=30°, m∠MFJ=50° , Find: Measurement of Arc KL & Measurement of Arc MJ

Answer 1

Part a) The measurement of arc KL is
`20\°`

Part b) The measurement of arc MJ is
`80\°`

Explanation:

Let

x--------> the measure of arc KL

y-------> the measure of arc MJ

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

`m<MEJ=(1)/(2)(y-x)`

substitute the given value

`30\°=(1)/(2)(y-x)`

`60\°=(y-x)`

`y=60\°+x` ------> equation A

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite.

`m<MFJ=(1)/(2)(x+y)`

substitute the given value

`50\°=(1)/(2)(x+y)`

`100\°=(x+y)`

`y=100\°-x` ------> equation B

Equate the equation A and B and solve for x

`60\°+x=100\°-x`

`2x=100\°-60\°`

`x=20\°`

Find the value of y

`y=100\°-20\°=80\°`

therefore

The measurement of arc KL is
`20\°`

The measurement of arc MJ is
`80\°`