Question

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

Answer 1

Answer:

20 degrees

Step-by-step explanation:

If you look at the central angles and then look at the other angles further you will see:

5+5=10

1*2=2

10*2=20

Answer 2

Answer:

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

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

Step-by-step 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.

$m$

substitute the given value

$30\°=\frac{1}{2}(y-x)$

$60\°=(y-x)$

$y=60\°+x$ ------> equation A

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

$m$

substitute the given value

$50\°=\frac{1}{2}(x+y)$

$100\°=(x+y)$

$y=100\°-x$ ------> 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 $80\°$