Question

in the circle, m∠S=33°, mRS=120, and RU is a tangent. the diagram is not drawn to scale. what is m∠U? Please help!

Answer 1

∠ U = 27°

Explanation:

The inscribed angle S is half the measure of its intercepted arc, thus

arc RT = 2 × ∠ U = 2 × 33³ = 66°

The secant- tangent angle U is half the measure of the difference of the measures of the intercepted arcs, that is

∠ U = 0.5( RS - RT) = 0.5(120 - 66)° = 0.5 ×54° = 27°

Answer 2

27°

Explanation:

arc RT = 66

1/2(120 - 66) = 27