Question

················Find m

Answer 1

Answer:

Step-by-step explanation:

There is a relationship if you have two lines intersecting a circle  and forming an angle outside of it.  In this instance.  There is a large arc, a small arc and the outside angle.  The relationship is (L-S)/2 = A, so large arc minus small arc all over 2 equals that outside angle.  

In this case the outside angle is U, the small arc is RT and the large arc is RS.  It gives us RS but we need RT.  There is another relationship to know, and that is that of an inscribed angle.  Or in other words if an angle is made inside a circle  and the two lines touch the circle at two other points.  We have that here  with angle S being an inscribed angle and making the arc RT, what we need to find.

The relationship for an inscribed angle is the inscribed angle = .5* arc angle.  So we can find the arc angle RT.

If we call the arc angle A and the inscribed angle I we can rewrite what I put before as I = .5A and then as I/.5 = A since we want to find the arc.  This can also be written as 2I = A

U = (SR-RT)/2

U = (SR - 2*S)/2

U = (82 - 2*22)/2

U = 19

If you want further explanation onto how the relationships I described worked I'd be happy to explain or perhaps link a video.