Question

Find the measure of the arc or angle indicated. Assume that lines which appeartangent are tangent.?KL240°

Answer 1

Based on the given diagram, the measure of the arc can be computed using the definition of a circle. One complete revolution of a circle is equal to 360 degrees. If given that we have the arc LJ equal to 240 degrees, the remaining arc, let as x, can be computed as

`x+240=360`

Solve for the value of x, we get

`x=360-240=120`

Finally, to solve for the angle K, we just divide the solved arc measure by half of it, getting

`m\angle K=(120)/(2)=60`

Hence, the measure of angle K is 60 degrees while the measure of the arc that corresponds to angle K is 120 degrees.