line segment xy is tangent to circle z at point u. if the measure of arc uv is 84°, what is the measure of…

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? 42° 84° 96° 168°

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? 42° 84° 96° 168°

Answer

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: Apply the formula

Let $\angle YUV$ be the angle formed by tangent $XY$ and chord $UV$. The intercepted arc is $\overset{\frown}{UV}$ with measure $m\overset{\frown}{UV}=84^{\circ}$. Then $m\angle YUV=\frac{1}{2}m\overset{\frown}{UV}$. $m\angle YUV=\frac{1}{2}\times84^{\circ}$

Answer:

$42^{\circ}$