Consider circle H with a 5 centimeter radius. If the length of major arc RST is 25/3π, what is the measure of ∠RST?
Given the major arc and the minor arc share the same chord, the angle RST will be:
The circumference of the circle will be 2pi (5) = 10 pi cm
So the measure of arc RST can be found as
(25/3) pi / [10 pi ] = arc RST / 360
25/30 = arc RST / 360
5/6 = arc RST /360
(5/6)360 = arc RST
300° = arc RST
Then minor arc RT = 60°
And since angle RST is an inscribed angle intercepting minor arc RT, its measure is (1/2) 60° = 30°
Just as bigbrotheprodude found....!!!!