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Consider circle H with a 5 centimeter radius. If the length of major arc RST is 25/3π, what is the measure of ∠RST?

kalab54 Feb 20, 2019

#1**+1 **

Given the major arc and the minor arc share the same chord, the angle RST will be:

∠RST=1/2∠RHT

∠RHT=1/3π=1/3×180=60

hence

∠RST=1/2×60=30°

Answer: 30°

bigbrotheprodude Feb 20, 2019

#2**+3 **

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....!!!!

CPhill Feb 21, 2019