Question

Can somebody explain this please

Answer 1

In this circle we have major arc RQ which is the really big one measuring 40x, and we have minor arc RQ, which is what we are looking for.  Minor arc RQ is double the measure of the angle that intercepts it.  That means that minor arc RQ is 2(12x-12), which is 24x - 24.  The measure of the outside of any circle will always and forever be 360 degrees;  therefore, 40x + 24x - 24 = 360.  Combining like terms gives us 64x = 384 and x = 6.  Now sub in that 6 for the x in the angle 12x - 12 to get that that angle measures 12(6)-12 = 60.  Again, the angle is half the measure of the arc it intercepts, so minor arc RQ is 120 degrees, third choice down.