Question

line segment xy is tangent to circle z at point u. if the measure of arc uv is 84°, what is the measure of ∠yuv? 96° 84° 42° 168°

Explanation:

Step1: Recall tangent - secant angle formula

The measure of an angle formed by a tangent and a secant is half the measure of the intercepted arc.

Step2: Identify the intercepted arc

The intercepted arc for $\angle YUV$ is $\overset{\frown}{UV}$, and $m\overset{\frown}{UV}=84^{\circ}$.

Step3: Calculate the angle measure

By the formula $m\angle YUV=\frac{1}{2}m\overset{\frown}{UV}$. Substitute $m\overset{\frown}{UV} = 84^{\circ}$ into the formula: $m\angle YUV=\frac{1}{2}\times84^{\circ}=42^{\circ}$.

Answer:

$42^{\circ}$