Applying the inscribed angle theorem, the missing angles are:
What is the Inscribed Angles Theorem?
Based on the inscribed angle theorem, we have the following relationships:
- Inscribed angle = 1/2(measure of intercepted arc)
- Central angle = measure of intercepted arc.
Given the following:
Find m(RS):
m(RS) = 180 - m(RU)
Substitute
m(RS) = 180 - 50
m(RS) = 130°
Find m∠RUS:
m∠RUS = 1/2(m(RS) [inscribed angle theorem]
Substitute
m∠RUS = 1/2(130)
m∠RUS = 65°
Find m∠UST:
m∠UST = 1/2(m(UT))
Substitute
m∠UST = 1/2(30)
m∠UST = 15°
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