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 ∠xuv? 42° 84° 96° 168°

Explanation:

Step1: Recall tangent - arc relationship

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

Step2: Identify the intercepted arc

The angle ∠XUV is formed by the tangent XY and the chord UV. The intercepted arc is $\overset{\frown}{UV}$, and its measure is given as 84°.

Step3: Calculate the measure of ∠XUV

By the tangent - chord angle rule, if the measure of the intercepted arc is $m\overset{\frown}{UV}$, then the measure of the angle formed by the tangent and the chord is $\frac{1}{2}m\overset{\frown}{UV}$. So, $m\angle XUV=\frac{1}{2}\times84^{\circ}=42^{\circ}$.

Answer:

$42^{\circ}$