Question

m<s=30°,mRS(arch)=84 degrees and RU is tangent to the circle at R. Find m<U. The figure is not drawn to scale. A) 27°
B) 12°
C) 54°
D) 24°

Answer 1

The correct answer among the choices provided is option B. Resulting angle m < U is equivalent to 12 °.

The first step is determine ∠SRU,
180° - 84° = 96° 
98°/2 = 48° 
∠SRU = 48° + 90° = 138° 

Then angle U from the triangle was determined using this formula,
∠U = 180° - ∠SRU - ∠S 
= 180° - 138° - 30° 
= 12°

Answer 2

Answer:

B. $12^{\circ}$

Step-by-step explanation:

We have been given an image of a circle. We are asked to find the measure of angle U.

We have been given that measure of angle 's' is 30 degrees, so the measure of arc RT will be 2 times the measure of angle 's' as angle 's' is inscribed angle of arc RT.

$\text{Measure of arc RT}=2\times 30^{\circ}$

$\text{Measure of arc RT}=60^{\circ}$

We know that the measure of angle formed by intersecting secant and tangent outside a circle is half the difference of intercepted arcs.

Using Secant-tangent theorem, we can set an equation to find the measure of angle U as:

$m\angle U=\frac{1}{2}\times (\text{Measure of arc RS}-\text{Measure of arc RT})$

Substituting the given values in above equation we will get,

$m\angle U=\frac{1}{2}\times(84^{\circ}-60^{\circ})$

$m\angle U=\frac{1}{2}\times(24^{\circ})$

$m\angle U=12^{\circ}$

Therefore, the measure of angle U is 12 degrees and option B is the correct choice.