Question

Given that LM and LN are tangent to the circle and that the measure of angle MLN = 75.86, find the measure of arc MN.

Answer 1

we know that

The measure of the external angle is the semidifference of the arcs that it covers

so

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

Let

x------> minor arc MN

major arc MN=360-x

substitute in the formula above

∠MLN=(1/2)*(mayor arc MN-minor arc MN)

75.86=(1/2)*(360-x-x)------> 151.72=(360-2x)------>360-151.72=2x

x=104.14°

therefore

the answer is

the measure of arc MN (minor arc) is 104.14°