Question

line segment xy is tangent to circle z at point u. if the measure of (overline{uv}) is (84^circ), what is the measure of (angle yuv)? (42^circ) (84^circ) (96^circ) (168^circ)

Explanation:

Step1: Recall tangent-chord angle theorem

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

Step2: Calculate $\angle YUV$

$\angle YUV = \frac{1}{2} \times m\overset{\frown}{UV}$
Substitute $m\overset{\frown}{UV}=84^\circ$:
$\angle YUV = \frac{1}{2} \times 84^\circ = 42^\circ$

Answer:

42°